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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)
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
} {\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
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
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
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
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
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
Software application
rectified imagery plans, true ortho-projections on planar, cylindric and conic surfaces, 3D photorealistic models, measurements from photography and mappings
Metigo
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
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
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
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
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
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
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 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
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
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
geometry) Brahmagupta theorem (Euclidean geometry) Brianchon's theorem (conics) British flag theorem (Euclidean geometry) Butterfly theorem (Euclidean
List_of_theorems
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
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
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
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
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
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
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
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
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
Mathematician
Jeanblanc, M. and Vrins, F. (2020). SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions. Stochastic Processes
Damiano_Brigo
Julia software and development tools
Modeling language for Mathematical Optimization (linear, mixed-integer, conic, semidefinite, nonlinear) · GitHub". github.com. Retrieved July 13, 2026
List of Julia software and tools
List_of_Julia_software_and_tools
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
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
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
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
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