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Term in mathematics
In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That
Complete_intersection
algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections. Informally
Complete_intersection_ring
scheme, then B is a complete intersection ring. The notion is used, for instance, in an essential way in Fulton's approach to intersection theory. The important
Regular_embedding
Algebraic structure
Any regular local ring is a complete intersection ring, but not conversely. A ring R is a set-theoretic complete intersection if the reduced ring associated
Commutative_ring
Type of surface in algebraic geometry
type that are not related to a product of two curves and are not a complete intersection of divisors in an Abelian variety. The Fano surface S of a smooth
Fano_surface
Construct in algebraic geometry
smoothable complete intersection morphism, this complex is perfect. Furthermore, if g : Y → Z is another smoothable complete intersection morphism and
Cotangent_complex
Concept in algebraic geometry
) {\displaystyle {\mathcal {O}}_{X}(-n{-}1{+}d)} . For a smooth complete intersection i : X ↪ P S n {\displaystyle i:X\hookrightarrow \mathbb {P} _{S}^{n}}
Adjunction_formula
Algebraic curve in projective 3-space
projective variety that is not linear or a hypersurface, in fact not a complete intersection. It is the three-dimensional case of the rational normal curve,
Twisted_cubic
Well-behaved sequence in a commutative ring
sense. This is the algebraic analogue of the geometric notion of a complete intersection. Given a commutative ring R and an R-module M, an element r in R
Regular_sequence
Tool in mathematical dimension theory
hypersurfaces, one after the other. A projective algebraic set is a complete intersection if its defining ideal is generated by a regular sequence. In this
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
Set of elements common to all of some sets
In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing
Intersection_(set_theory)
Concept in algebraic geometry
complete intersections of algebraic hypersurfaces whose sum of degrees is at most the total dimension of the ambient projective space. Such complete intersections
Fano_variety
\mathbb {Z} /2\to 0} Consider a smooth complete intersection 3-fold X {\displaystyle X} (such as a complete intersection Calabi-Yau 3-fold). If we look at
Atiyah–Hirzebruch spectral sequence
Atiyah–Hirzebruch_spectral_sequence
Road junction where two or more roads either meet or cross at grade
An intersection, crossroads, or at-grade junction is a junction where two or more roads converge, diverge, meet or cross at the same height, as opposed
Intersection_(road)
Local ring in commutative algebra
Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A Gorenstein ring is a commutative Noetherian
Gorenstein_ring
Riemannian manifold with SU(n) holonomy
An overview of Calabi-Yau Elliptic fibrations Lectures on the Calabi-Yau Landscape Fibrations in CICY Threefolds - (complete intersection Calabi-Yau)
Calabi–Yau_manifold
PSPACE-complete decision problem from the field of automata theory. The problem asks if a list of deterministic finite automata has nonempty intersection. A
Intersection non-emptiness problem
Intersection_non-emptiness_problem
Type of ring in commutative algebra
Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings There are a number of useful definitions
Regular_local_ring
Graph representing intersections between given sets
an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph
Intersection_graph
Type of commutative ring in mathematics
Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings For a commutative Noetherian local ring
Cohen–Macaulay_ring
Problem in algebraic geometry
algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection ⋂ i = 1 r X i {\displaystyle \bigcap _{i=1}^{r}X_{i}}
Residual_intersection
Mazur defined a morphism to be syntomic if it is flat and locally a complete intersection. The syntomic topology is generated by surjective syntomic morphisms
Syntomic_topology
On decreasing nested sequences of non-empty compact sets
Cantor's intersection theorem, also called Cantor's nested intervals theorem, refers to two closely related theorems in general topology and real analysis
Cantor's_intersection_theorem
At-grade road junction in which cyclists and pedestrians are separated from cars
A protected intersection or protected junction, also known as a Dutch-style junction, is a type of at-grade road junction in which cyclists and pedestrians
Protected_intersection
Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings Suppose that A is a Noetherian domain
Catenary_ring
Topological model
The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions (two
DE-9IM
Generalized notion of counting curve intersections
In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves
Intersection_number
Type of road intersection
vehicles behind a completed turn into the crossroad without any conflict to oncoming traffic. On the crossroad, the four-leg intersection is replaced by
Split_intersection
In algebraic geometry, the scheme-theoretic intersection of closed subschemes X, Y of a scheme W is X × W Y {\displaystyle X\times _{W}Y} , the fiber product
Scheme-theoretic_intersection
Enhancing visibility at intersections to improve safety
compliance with existing laws against parking near intersections. Traffic calming Curb extension Complete streets Vision Zero Transportation planning Urban
Intersection_daylighting
Diagonal intersection is a term used in mathematics, especially in set theory. If δ {\displaystyle \displaystyle \delta } is an ordinal number and ⟨ X
Diagonal_intersection
Theorem in geometry
Also, if f : X → Y {\displaystyle f:X\to Y} is a (global) local complete intersection morphism; i.e., it factors as a closed regular embedding X ↪ P {\displaystyle
Riemann–Roch-type_theorem
Complexity class
NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete when:
NP-completeness
Algebra, a branch of mathematics
Triangulated category Eisenbud, David (1980). "Homological Algebra on a Complete Intersection, with an Application to Group Respresentations" (PDF). Transactions
Matrix factorization (algebra)
Matrix_factorization_(algebra)
Traffic intersection
traffic only, above the main conventional roadway intersection. It is known as the Hovenring. Complete streets Direction of traffic History of road transport
Roundabout
3 p g − 7. {\displaystyle c_{1}^{2}=3p_{g}-7.} Complete intersections: A smooth complete intersection of hypersurfaces of degrees d 1 ⩾ d 2 ⩾ ⋯ ⩾ d n
Surface_of_general_type
curve is not a plane curve (since a hyperelliptic curve is never a complete intersection in a projective space). Over the complex numbers, C is a compact
Complete_algebraic_curve
In algebra, expression of an ideal as the intersection of ideals of a specific type
this implies that it is a complete intersection (more precisely, it defines an algebraic set, which is a complete intersection), and thus all primary components
Primary_decomposition
Romanian-American mathematician
Lawrence; Mustaţǎ, Mircea (2004). "Inversion of adjunction for local complete intersection varieties". American Journal of Mathematics. 126 (6): 1355–1365
Mircea_Mustață
British-American mathematician (born 1962)
that arose from this approach was also a complete intersection. This ring theoretic result essentially completed the proof of the semistable case of Taniyama-Shimura
Richard Taylor (mathematician)
Richard_Taylor_(mathematician)
Theorem in extremal set theory
(2004) Ahlswede, Rudolf; Khachatrian, Levon H. (1996). "The complete nontrivial-intersection theorem for systems of finite sets". Journal of Combinatorial
Ahlswede–Khachatrian_theorem
Mathematical term
mathematics, a field K with an absolute value is called spherically complete if the intersection of every decreasing sequence of balls (in the sense of the metric
Spherically_complete_field
American technology and advertising company
Intersection is a smart cities technology and out-of-home advertising company. It was formed as a result of a merger between Control Group and Titan in
Intersection_(company)
Type of road intersection with three arms
three-way junction (or three-way intersection) is a type of road intersection with three arms. A Y junction (or Y intersection) generally has three arms of
Three-way_junction
Algebraic geometry scheme
Cartier and X is Cohen–Macaulay. An algebraic variety with local complete intersection singularities, for example any hypersurface in a smooth variety
Gorenstein_scheme
Upper bound on intersecting set families
Grindstaff (2020). Ahlswede, Rudolf; Khachatrian, Levon H. (1997), "The complete intersection theorem for systems of finite sets", European Journal of Combinatorics
Erdős–Ko–Rado_theorem
2021 EP by BDC
The Intersection: Contact (stylized in all caps) is the third extended play by South Korean boy band BDC and the final release from their The Intersection
The_Intersection:_Contact
Mathematical technique
Eisenbud, David (1980-01-01). "Homological algebra on a complete intersection, with an application to group representations". Transactions of
Matrix factorization of a polynomial
Matrix_factorization_of_a_polynomial
Scheme in algebraic geometry
} Example: One has that X {\displaystyle X} is a local complete intersection if and only if C X = N X {\displaystyle {\mathfrak {C}}_{X}={\mathfrak
Normal cone (algebraic geometry)
Normal_cone_(algebraic_geometry)
3y^{2}-dy)}}\right).} Note that since the left term in the derived intersection is a complete intersection, we can compute a complex representing the derived ring
Derived_scheme
Road junction
Ratchathewi Intersection (Thai: แยกราชเทวี, RTGS: Yaek Ratchathewi, pronounced [jɛ̂ːk râːt.tʰēː.wiː]) is a four-way intersection of Phaya Thai and Phetchaburi
Ratchathewi_Intersection
Graph property
the latter without necessarily having a large automorphism group. The intersection array of a distance-regular graph is the array ( b 0 , b 1 , … , b d
Distance-regular_graph
Type of road intersections
offset T-intersection is an at-grade road intersection where a conventional four leg intersection is split into two three-leg T-intersections to reduce
Offset_T-intersection
German mathematician (born 1937)
893. Forster, Otto (1984). "Complete intersections in affine algebraic varieties and Stein spaces". Complete Intersections. Lecture Notes in Mathematics
Otto_Forster
Danish mathematician (1947–2014)
Alzheimer's disease on 8 April 2014. Sather-Wagstaff, Keri Ann. "Complete intersection dimensions and Foxby classes" (PDF). Journal of Pure and Applied
Hans-Bjørn_Foxby
Mathematics concept
"Hodge diamond of complete intersections". math.stackexchange.com. Retrieved 2017-03-06. "Cohomology tables for complete intersections". pbelmans.ncag.info
Homological_mirror_symmetry
Geometric figure made of 4 points connected by 6 lines
Dually, a complete quadrilateral is a system of four lines, no three of which pass through the same point, and the six points of intersection of these
Complete_quadrangle
Area of discrete mathematics
sets have a nonempty intersection. Each vertex is represented as a set, and every two vertices are connected. Hence, the intersection graph of finite sets
Graph_theory
Intersection Capacity Utilization (ICU) method is a tool for measuring a roadway intersection's capacity. It is ideal for transportation planning applications
Intersection capacity utilization
Intersection_capacity_utilization
Data type for values having two types
In type theory, an intersection type can be allocated to values that can be assigned both the type σ {\displaystyle \sigma } and the type τ {\displaystyle
Intersection_type
Type of smooth complex surface of kodaira dimension 0
\mathbf {P} ^{5}} is a K3 surface of genus 5 (that is, degree 8). The complete intersection of two bihomogeneous forms of bidegrees ( 1 , 2 ) {\displaystyle
K3_surface
Process in algebraic geometry
Nash blowing-up is locally a monoidal transformation. If X is a complete intersection defined by the vanishing of f 1 , f 2 , … , f n − r {\displaystyle
Nash_blowing-up
not parafactorial, even if they are factorial. Every Noetherian complete intersection local ring of dimension at least 4 is parafactorial. For a locally
Parafactorial_local_ring
curve can be obtained as the intersection of two quadrics. In general abelian varieties are not complete intersections. Computer algebra techniques are
Equations defining abelian varieties
Equations_defining_abelian_varieties
noetherian, dimension, catenary, Gorenstein. local complete intersection The local rings are complete intersection rings. See also: regular embedding. local uniformization
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Type of three-way road intersection
A seagull intersection or continuous green T-intersection (also called a turbo-T (in Florida) or High-T intersection (in Nevada and Utah)) is a type of
Seagull_intersection
Fewest cliques covering a graph's edges
In the mathematical field of graph theory, the intersection number of a graph G = ( V , E ) {\displaystyle G=(V,E)} is the smallest number of elements
Intersection number (graph theory)
Intersection_number_(graph_theory)
as the intersection graph of congruent spheres. The sphericity of a graph is one of several notions of graph dimension based on intersection graphs;
Sphericity_(graph_theory)
Branch of type theory
mathematical logic, the intersection type discipline is a branch of type theory encompassing type systems that use the intersection type constructor ( ∩
Intersection_type_discipline
situation should be emulated for a simple case (such as a smooth complete intersection). Suppose we have a variety X {\displaystyle X} (representing the
Virtual_fundamental_class
Theory for associative algebras over rings
Hochschild homology not just for smooth algebras, but also for local complete intersection algebras. In this case, given a presentation A = R / I {\displaystyle
Hochschild_homology
algebraic surfaces, which are hypersurfaces in P3, or more generally complete intersections. It states that, for degree at least four for hypersurfaces, the
Max Noether's theorem on curves
Max_Noether's_theorem_on_curves
Algebraic structure
satisfies (ii). Geometrically, we have the following: if X is a local complete intersection in a nonsingular variety; e.g., X itself is nonsingular, then X
Integrally_closed_domain
Theorem in topology
intersection theorem is a result in general topology that gives a sufficient condition for a nested sequence of sets to have a non-empty intersection
Kuratowski's intersection theorem
Kuratowski's_intersection_theorem
Type of intersection
Michigan left or P-turn is an at-grade intersection design that replaces each left (farside) turn at an intersection between a (major) divided roadway and
Michigan_left
Spanish mathematician and professor
(Birkhäuser 2007) and co-authored the monograph Gorenstein Liaison, Complete Intersection Liaison Invariants and Unobstructedness (American Mathematical Society
Rosa_M._Miró-Roig
Concept in mathematical logic
In mathematical logic, a theory of a language is complete if it is consistent and it proves every closed formula with which it is not inconsistent. That
Complete_theory
quadrics that generate the ideal of the curve. The curve is not a complete intersection, for n > 2. That is, it cannot be defined (as a subscheme of projective
Rational_normal_curve
ring is a ring that is a coherent module over itself. complete 1. A local complete intersection ring is a Noetherian local ring whose completion is the
Glossary of commutative algebra
Glossary_of_commutative_algebra
Fewest edge crossings in drawing of a graph
Society). 7: 68–72. Saaty, T.L. (1964). "The minimum number of intersections in complete graphs". Proceedings of the National Academy of Sciences of the
Crossing number (graph theory)
Crossing_number_(graph_theory)
Topics referred to by the same term
configuration of 20 planes and all their 3-fold (or higher) points of intersection (and optionally, depending on your understanding of a configuration,
Complete_icosahedron
Process in mathematics
after the French mathematician Jean-Louis Koszul. Koszul duality Complete intersection ring Fröberg, R. (1999), "Koszul algebras", Advances in commutative
Koszul_algebra
American writer and biochemist (1920–1992)
assume complete ignorance of the subjects on the part of his readers. The column was ostensibly dedicated to popular science but Asimov had complete editorial
Isaac_Asimov
Generalization of a vector bundle
embedding of the normal cone into the normal bundle. Consider the complete intersection ideal ( f , g 1 , g 2 , g 3 ) ⊂ C [ x 0 , … , x n ] {\displaystyle
Cone_(algebraic_geometry)
Metric geometry
complete metric inducing the given topology. Completely metrizable spaces can be characterized as those spaces that can be written as an intersection
Complete_metric_space
Type of road intersection
for the left turn prohibition at the main intersection. As of 2007[update] no agency has designed a complete bowtie road junction. Hamburger
Bowtie_(road)
Commutative algebra studies commutative rings, their ideals, and modules over such rings
Projective module Injective module Cohen-Macaulay ring Gorenstein ring Complete intersection ring Koszul complex Hilbert's syzygy theorem Quillen–Suslin theorem
List of commutative algebra topics
List_of_commutative_algebra_topics
Nullstellensatz Complete variety Elimination theory Gröbner basis Projective variety Quasiprojective variety Canonical bundle Complete intersection Serre duality
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Type of high capacity intersection
A superstreet is a type of road intersection that is a variation of the Michigan left. In this configuration, in contrast to the Michigan left, traffic
Superstreet
Partially ordered set in which all subsets have both a supremum and infimum
trivially complete. The power set of a given set when ordered by inclusion. The supremum is given by the union and the infimum by the intersection of subsets
Complete_lattice
On topological spaces where the intersection of countably many dense open sets is dense
topological space to be a Baire space (a topological space such that the intersection of countably many dense open sets is still dense). It is used in the
Baire_category_theorem
Calabi–Yau quintic 3-folds can be applied to arbitrary Calabi–Yau complete intersections using the generalized A {\displaystyle A} -hypergeometric functions
Combinatorial_mirror_symmetry
Russian American mathematician
proof of the mirror conjecture for Calabi–Yau manifolds that are complete intersections in toric ambient spaces, in particular for quintic hypersurfaces
Alexander_Givental
Nonexistence of gaps in the number line
that bn − an → 0 as n → +∞. The nested interval theorem states that the intersection of all of the intervals In contains exactly one point. For any ordered
Completeness of the real numbers
Completeness_of_the_real_numbers
Movement of vehicles and pedestrians along land routes
well-established priorities, lanes, right-of-way, and traffic control at intersections. (International Regulations for Preventing Collisions at Sea govern
Traffic
Objects of certain abelian categories associated to topological spaces
system F {\displaystyle {\mathcal {F}}} . If X is a flat, locally complete intersection (for example, regular) scheme over a henselian discrete valuation
Perverse_sheaf
Type of roadway junction with one main intersection and two secondary intersections
roadway intersection adds an additional "quadrant roadway" between two legs of an intersection. This roadway adds two three-way intersections in addition
Quadrant_roadway_intersection
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
The second deviation ε2 vanishes exactly when the ring R is a complete intersection ring, in which case all the higher deviations vanish. Gulliksen
Deviation_of_a_local_ring
Russian/American mathematician (born 1949)
Vayntrub. Libgober's early work studies the diffeomorphism type of complete intersections in complex projective space. This later led to the discovery of
Anatoly_Libgober
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