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In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution to a Cartesian equation of the form: X 2 + a X Y + b Y 2 = P (
Conic_bundle
Subfield of mathematical optimization
i=1,\dots ,p,\end{aligned}}} Every convex program can be presented in a conic form, which means minimizing a linear objective over the intersection of
Convex_optimization
Subfield of convex optimization
matrices. The code ConicBundle formulates the SDP problem as a nonsmooth optimization problem and solves it by the Spectral Bundle method of nonsmooth
Semidefinite_programming
Family of geometric objects with a common property
object can be used in a pencil. The common ones are lines, planes, circles, conics, spheres, and general curves. Even points can be used. A pencil of points
Pencil_(geometry)
Russian mathematician (born 1950)
criterion provided the Iskovskikh's criterion for rationality of a standard conic bundle whose base is a smooth minimal rational surface. Since the late 80's
Vyacheslav_Shokurov
Algebraic surface
{\displaystyle y^{2}-az^{2}=P(x),\,} where P has degree 3 or 4. They are conic bundles. Châtelet, F. (1959), "Points rationnels sur certaines courbes et surfaces
Châtelet_surface
Techniques in mathematical analysis
occurs is encoded by the wave front set of a distribution, a conic subset of the cotangent bundle with the zero section removed. Microlocal analysis was developed
Microlocal_analysis
Topics referred to by the same term
vertical plane Conic section, intersection of a cone and a plane Section (category theory), a right inverse of some morphism Section (fiber bundle), in topology
Section
Subspace defined by a polynomial of degree 2 over a field
quadric curve in P 2 {\displaystyle \mathbf {P} ^{2}} is called a conic. A split conic over k is isomorphic to the projective line P 1 {\displaystyle \mathbf
Quadric_(algebraic_geometry)
hdl:2433/214762. ISSN 0894-0347. JSTOR 30041435. Prokhorov, Yuri (1996). "On the general elephant conjecture for Mori conic bundles". arXiv:alg-geom/9608007. v t e
General_elephant
canonical line bundle. point-star A family of lines with a common point polar 1. (Adjective) Related by a polarity 2. The polar conic is the zero set
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Non-tensorial representation of the spin group
space of signature (1,2), the conic is an ordinary real conic (here the circle), the line bundle is the Möbius bundle, and the spin group is SL2(R).
Spinor
Problem in algebraic geometry
are the solutions to problems in enumerative geometry (e.g., Steiner's conic problem) and the derivation of the multiple-point formula, the formula allowing
Residual_intersection
Concept in algebraic geometry
five points determine a conic, but in general six points do not lie on a conic, so being in general position with respect to conics requires that no six
General_position
Abelian group related to division algebras
dimension 1 are exactly the smooth conics in the projective plane over K. For a field K of characteristic not 2, every conic over K is isomorphic to one of
Brauer_group
Branch of geometry
structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently
Contact_geometry
State of matter with properties of both conventional liquids and crystals
properties. There are three types of thermotropic liquid crystals: discotic, conic (bowlic), and rod-shaped molecules. Discotics are disc-like molecules consisting
Liquid_crystal
Study of mathematical algorithms for optimization problems
quadratic programming. Conic programming is a general form of convex programming. LP, SOCP and SDP can all be viewed as conic programs with the appropriate
Mathematical_optimization
to the absolute conic on the plane at infinity. Using the absolute dual quadric and its projection, the dual image of the absolute conic The modulus constraint
Camera_auto-calibration
Process of estimating the parameters of a pinhole camera model
self-calibration techniques are applied to obtain the image of the absolute conic matrix. The main contribution of Zhang's method is how to, given n {\displaystyle
Camera_resectioning
Field of algebraic geometry
canonical bundle of a smooth variety X of dimension n means the line bundle of n-forms KX = Ωn, which is the nth exterior power of the cotangent bundle of X
Birational_geometry
Concept in algebraic geometry
Pezzo surface is a complete non-singular surface with ample anticanonical bundle. There are some variations of this definition that are sometimes used. Sometimes
Del_Pezzo_surface
of the tautological line bundle O X ( − 1 ) {\displaystyle {\mathcal {O}}_{X}(-1)} . It is also called the hyperplane bundle. O X ( D ) {\displaystyle
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Moduli space in the Grothendieck category of schemes
moduli space of special instanton bundles, in mathematical physics, with objects in the classical geometry of conics, in certain cases. "Moduli theory"
Moduli_scheme
Group of real 2×2 matrices with unit determinant
and is a squeeze mapping. The names correspond to the classification of conic sections by eccentricity: if one defines eccentricity as half the absolute
SL2(R)
varieties are conics. The corresponding central simple algebras are the quaternion algebras. The algebra (a, b)K corresponds to the conic C(a, b) with
Severi–Brauer_variety
Intersection of a torus and a plane
two congruent conics, which are the two Villarceau circles. Hirsch extends this argument to any surface of revolution generated by a conic and shows that
Villarceau_circles
Branch of mathematics
the use of projective geometry to create forced perspective, the use of conic sections in constructing domes and similar objects, the use of tessellations
Geometry
Curve whose normals converge asymptotically
hyperboloid with planes that generate parabolas on the asymptotic cone (see conic sections " the cutting plane is parallel to exactly one generating line
Horocycle
Species of conifer
(8–14 inches) long, and distinctly yellowish green. The cones are ovoid conic, 12–24 cm (4+1⁄2–9+1⁄2 in) long and 5–8 cm (2–3 in) broad at the base when
Pinus_roxburghii
} {\displaystyle \{(x,0):x\neq 0\},\{(0,y):y\neq 0\}} , and the affine conics given by x y = a {\displaystyle xy=a} for some a ∈ C ∗ {\displaystyle a\in
GIT_quotient
Concept in algebraic geometry
line bundle or invertible sheaf language. In those terms, divisors D {\displaystyle D} (Cartier divisors, to be precise) correspond to line bundles, and
Linear_system_of_divisors
class used in the study of cones, a generalization of vector bundles. For vector bundles the total Segre class is inverse to the total Chern class, and
Segre_class
Model of the extended complex plane plus a point at infinity
connects most readily to projective geometry. For example, any line (or smooth conic) in the complex projective plane is biholomorphic to the complex projective
Riemann_sphere
Degree of differentiability of a function or map
p}:T_{p}M\to T_{F(p)}N,} and on the level of the tangent bundle, the pushforward is a vector bundle homomorphism: F ∗ : T M → T N . {\displaystyle F_{*}:TM\to
Smoothness
Genus of fruits and plants
two ovules per pistil; the style and stigma are club-shaped or narrowly conic. One fleshy, ovate to spherical fruit is produced per flower. Each fruit
Annona
German mathematician
Reye worked on conic sections, quadrics and projective geometry. Reye's work on linear manifolds of projective plane pencils and of bundles on spheres influenced
Theodor_Reye
Research program on the symmetries of geometry
appropriate concepts, thus for example projective geometry rightly talked about conic sections, but not about circles or angles because those notions were not
Erlangen_program
Species of flowering plant
species: Cuscuta California var. apiculata – This variety has an ovoid to conic shaped ovary and fruit, with a pointed tip, and one seed. Cuscuta californica
Cuscuta_californica
Theory in physics
2875. Similarly, the Donaldson–Thomas invariant of the moduli space of conics on the quintic is 609250. For a Calabi–Yau threefold Y {\displaystyle Y}
Donaldson–Thomas_theory
Type of differential equation
second-order in that region. This form is analogous to the equation for a conic section: A x 2 + 2 B x y + C y 2 + ⋯ = 0. {\displaystyle Ax^{2}+2Bxy+Cy^{2}+\cdots
Partial_differential_equation
Segre embedding of a product of projective spaces Rational normal curve Conics, Pascal's theorem, Brianchon's theorem Twisted cubic Elliptic curve, cubic
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Concept in mathematics
set of polynomials (unlike the affine case). For example, let X be the conic y 2 = x z {\displaystyle y^{2}=xz} in P2. Then two maps ( x : y : z ) ↦
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
pustules. pyramidal (of a growth habit) Shaped like an Egyptian pyramid, broad conic with a quadrate cross-section. Not found in nature, in living things only
Glossary_of_botanical_terms
Mathematical model of the time dependence of a point in space
Poncelet map, where a point is moving in successive steps between two given conics, and the equations are algebraic (i.e. tangents and intersections). Another
Dynamical_system
Economic Model
is Pareto-better for the coalition, and since P P {\displaystyle PP} is conic, we also have ∑ i ( x ¯ i − r i ) ∈ P P S {\displaystyle \sum _{i}({\bar
Arrow–Debreu_model
All Latin and Greek roots beginning with G
constitution, corrode, quondam con- cone Greek κῶνος (kônos), κωνικός (kōnikós) conic, conical, conicoid, conodont, conoid, conoscope, orthocone, orthoconic,
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
unchanged under field extensions), whereas ruledness is not. For example, the conic x2 + y2 + z2 = 0 in P2 over the real numbers R is uniruled but not ruled
Ruled_variety
Completion of the usual space with "points at infinity"
they intersect in exactly one point. Also, there is only one class of conic sections, which can be distinguished only by their intersections with the
Projective_space
Machinery used to spin cotton
spinning machine in a poem in 1757: A circular machine, of new design In conic shape: it draws and spins a thread Without the tedious toil of needless
Cotton-spinning_machinery
Species of conifer
(66 ft) tall. The tree is broad conical when young, becoming columnar with a conic apex with age; younger specimens having ascending branches and older trees
Pinus_koraiensis
set is a single point iff the curve is a conic section. Note that in affine geometry, the focus of a conic section is not a meaningful concept, since
Affine_differential_geometry
List of topics related to π Pole and polar – Unique point and line of a conic section Power of a point – Relative distance of a point from a circle Radical
List_of_circle_topics
Surface with constant mean curvature
mean curvature were the surfaces obtained by rotating the roulettes of the conics. These are the plane, cylinder, sphere, the catenoid, the unduloid and nodoid
Constant-mean-curvature surface
Constant-mean-curvature_surface
Software application
rectified imagery plans, true ortho-projections on planar, cylindric and conic surfaces, 3D photorealistic models, measurements from photography and mappings
Metigo
Singularities of algebraic varieties
power line bundle ω X ⊗ m {\displaystyle \omega _{X}^{\otimes m}} on X smooth {\displaystyle X^{\text{smooth}}} extends to a line bundle on X. The main
Canonical_singularity
geometry) Brahmagupta theorem (Euclidean geometry) Brianchon's theorem (conics) British flag theorem (Euclidean geometry) Butterfly theorem (Euclidean
List_of_theorems
Algebraic surface defined by a cubic polynomial
position, meaning that no three points lie on a line and all 6 do not lie on a conic. As a complex manifold (or an algebraic variety), the surface depends on
Cubic_surface
Intersection theory. In 1848 Steiner claimed that the number of conics tangent to 5 given conics is 7776 = 65, but later realized this was wrong. The correct
List_of_incomplete_proofs
Greek mathematician (1873–1950)
Jordan's Cours d'Analyse and Salmon's text on the analytic geometry of conic sections. He also visited the Cheops pyramid and made measurements which
Constantin_Carathéodory
Method to solve optimization problems
with an API for large scale optimization of linear, integer, quadratic, conic and general nonlinear programs with stochastic programming extensions. It
Linear_programming
Pressed together, narrowed. Concave – Excavated, hollowed out. Conchiolin Conic – Shaped like a cone. Connective – A part connecting two other parts, as
Glossary_of_gastropod_terms
Thomas, Richard P. (2006), "Notes on GIT and symplectic reduction for bundles and varieties", Surveys in Differential Geometry, 10 (1): 221–273, arXiv:math/0512411v3
Hilbert–Mumford_criterion
Museum in Rio de Janeiro, Brazil
limestone statue of a young woman, dated of the New Kingdom, carrying a conic ointment vessel on the top of her head – an iconography that is almost exclusively
National_Museum_of_Brazil
List of definitions of terms and concepts commonly used in aerospace engineering
The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
Mathematician
Jeanblanc, M. and Vrins, F. (2020). SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions. Stochastic Processes
Damiano_Brigo
Species of palm
is blunt and thickened. The anthers are white. The style is short, and conic in shape. The pedicel is 2-3mm long. The fruit is coloured glossy green
Livistona_tahanensis
American Catholic bishop (1814–1877)
seven to mathematics and natural science, including navigation, surveying, conic sections, mechanics, chemistry, astronomy, and optics; three to moral and
James_Roosevelt_Bayley
Sums of sets of vectors are nearly convex
the conic hull of { q ¯ n , k } n ∈ 1 : N , k ∈ 1 : K {\displaystyle \{{\bar {q}}_{n,k}\}_{n\in 1:N,k\in 1:K}} . By Carathéodory's theorem for conic hulls
Shapley–Folkman_lemma
Most na Adi" [Ada Bridge open with fireworks] (in Serbian). Blic. Igor Conić (8 February 2011). "Most na Adi u magazinu Bridge" [Ada Bridge in the Bridge
Bridges_of_Belgrade
CONIC BUNDLE
CONIC BUNDLE
Girl/Female
American, Arabic, Australian, British, Chinese, English
Stone of the Colic; The Gemstone Jade; Green in Colour
Surname or Lastname
English
English : of uncertain origin; possibly a topographic name for someone who lived where wormwood (Artemesia absinthium) grew, Middle English wormod, or a metonymic occupational name for a herbalist. In the Middle Ages wormwood was variously used as a tonic and vermifuge, in brewing ale, and to protect clothes and linen from moths and fleas.
Surname or Lastname
English (southwest)
English (southwest) : occupational name for a digger of ditches or a builder of dikes, or a topographic name for someone who lived by a ditch or dike, from an agent derivative of Middle English diche, dike (see Dyke).English : regional name from an area of East Sussex, near Hellingly, called ‘the Dicker’ (hence also the hamlets of Upper and Lower Dicker), from Middle English dyker unit of ten (Latin decuria, from decem ‘ten’); the reason for the place being so named is not clear. It has been suggested that the reference is to a bundle of iron rods, in which sense dicras appears in Domesday Book. Such a bundle could have been the rent for property in this iron-working area. Surname forms such as atte dicker occur in the surrounding region in the 13th and 14th centuries.German and Jewish (Ashkenazic) : variant of Dick 2, from an inflected form.North German : variant of Low German Dieker, a topographic or an occupational name for someone who lived or worked at a dike (see Dieck).Americanized spelling of French Decaire.
Surname or Lastname
English
English : from Old French balon ‘bundle’, ‘roll’, ‘pack’, hence a nickname for a small, rotund man or possibly a metonymic occupational name for a carrier of goods and merchandise.French (Bâlon) : generally regarded as a habitational name from Baalons in the Ardennes, it may however simply be from balon ‘ball’, ‘roll’ (see 1) or a derivative of Bal.
Surname or Lastname
English
English : occupational nickname for a peddler, from Old French trousse ‘bundle’, ‘pack’.Ukrainian : nickname from trus ‘rabbit’, typically applied to someone thought to be a coward.
Boy/Male
American, Arabic, Australian, French, Hebrew, Latin
Eloquent or Bundle of Grain; First Son; Long Living
Girl/Female
Gujarati, Hindu, Indian, Marathi, Telugu
Sunrise; Comic
Boy/Male
Indian
Bundle of Joy
Surname or Lastname
English
English : from Middle English pa(c)k ‘pack’, ‘bundle’ + the Anglo-Norman French pejorative suffix -ard, hence a derogatory occupational name for a peddler.English : pejorative derivative of the Middle English personal name Pack.English : from a Norman personal name, Pachard, Baghard, composed of the Germanic elements pac, bag ‘fight’ + hard ‘hardy’, ‘brave’, ‘strong’.Probably an Americanized spelling of German Packert, Päckert, from Germanic personal names formed with a word meaning ‘battle’ or ‘to fight’; or a variant of Packer 2 (with excrescent -t).
Surname or Lastname
English
English : from Middle English cony ‘rabbit’ (a back-formation from conies, from Old French conis, plural of conil), a nickname for someone thought to resemble a rabbit in some way or a metonymic occupational name for a dealer in rabbits or rabbit skins.
Surname or Lastname
English (Kent)
English (Kent) : from Middle English shefe ‘sheaf’, ‘bundle’ (Old English scēaf), hence possibly a metonymic occupational name for a harvest worker, or for someone who paid or collected tithes, from the same term in the sense ‘tenth’ (or other proportion of produce paid as a tithe).Jacob Sheafe (d. 1658) was one of the founds of Boston MA. He is buried in the King’s Chapel Burying Ground there.
CONIC BUNDLE
CONIC BUNDLE
Girl/Female
Arabic, Muslim
Beautiful
Girl/Female
Indian, Telugu, Traditional
Brave
Boy/Male
Hindu, Indian
Grace; Favor
Girl/Female
Tamil
Anukampa | அநà¯à®•à®®à¯à®ªà®¾
Gods grace
Boy/Male
Hindu
Boy/Male
American, Anglo, Australian, British, English, German, Teutonic
Glorious Raven; Bright Raven
Girl/Female
Gujarati, Indian, Kannada, Sanskrit
Heavenly Jewel
Girl/Female
Muslim
Proper name, Cloud that carries rain
Female
Hebrew
(תִּרְצָה) Hebrew name TIRTSAH means "pleasantness." In the bible, this is a place name and the name of a daughter of Zelophehad.
Boy/Male
Arabic, Muslim
Inhabited; Civilized
CONIC BUNDLE
CONIC BUNDLE
CONIC BUNDLE
CONIC BUNDLE
CONIC BUNDLE
n.
Conic sections.
n.
A verse or meter composed or consisting of Ionic feet.
a.
Pertaining to the Ionic order of architecture, one of the three orders invented by the Greeks, and one of the five recognized by the Italian writers of the sixteenth century. Its distinguishing feature is a capital with spiral volutes. See Illust. of Capital.
n.
Ionic type.
n.
A tonic element or letter; a vowel or a diphthong.
a.
Of or pertaining to tension; increasing tension; hence, increasing strength; as, tonic power.
a.
Alt. of Conical
n.
Lead colic.
n.
The Ionic volute.
n.
The Ionic dialect; as, the Homeric Ionic.
a.
A combining form, meaning somewhat resembling a cone; as, conico-cylindrical, resembling a cone and a cylinder; conico-hemispherical; conico-subulate.
n.
A foot consisting of four syllables: either two long and two short, -- that is, a spondee and a pyrrhic, in which case it is called the greater Ionic; or two short and two long, -- that is, a pyrrhic and a spondee, in which case it is called the smaller Ionic.
a.
Tonic.
a.
Comic, farcical.
n.
One of a sect or school of philosophers founded by Antisthenes, and of whom Diogenes was a disciple. The first Cynics were noted for austere lives and their scorn for social customs and current philosophical opinions. Hence the term Cynic symbolized, in the popular judgment, moroseness, and contempt for the views of others.
n.
A tonic.
a.
Of or pertaining to a cone; as, conic sections.
a.
Of or pertaining to colic; affecting the bowels.
n.
A conic section.
a.
Of or pertaining to the colon; as, the colic arteries.