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Kummer surface

Index Kummer surface

In algebraic geometry, a Kummer quartic surface, first studied by, is an irreducible nodal surface of degree 4 in \mathbbP^3 with the maximal possible number of 16 double points. [1]

22 relations: Abelian variety, Algebraic geometry, Bilinear form, Branched covering, Cambridge University Press, Canonical bundle, Genus (mathematics), Genus–degree formula, Hyperconnected space, Hyperelliptic curve, Jacobian variety, K3 surface, Kummer configuration, Kummer variety, Linear system, Nodal surface, Springer Science+Business Media, Tangent cone, Tetrahedroid, Theta divisor, Wave surface, Weddle surface.

Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Bilinear form

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.

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Branched covering

In mathematics, a branched covering is a map that is almost a covering map, except on a small set.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Canonical bundle

In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n.

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Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

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Genus–degree formula

In classical algebraic geometry, the genus–degree formula relates the degree d of an irreducible plane curve C with its arithmetic genus g via the formula: Here "plane curve" means that C is a closed curve in the projective plane \mathbb^2.

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Hyperconnected space

In mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two proper closed sets (whether disjoint or non-disjoint).

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Hyperelliptic curve

In algebraic geometry, a hyperelliptic curve is an algebraic curve given by an equation of the form where f(x) is a polynomial of degree n > 4 with n distinct roots.

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Jacobian variety

In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles.

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K3 surface

In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle.

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Kummer configuration

In geometry, the Kummer configuration, named for Ernst Kummer, is a geometric configuration of 16 points and 16 planes such that each point lies on 6 of the planes and each plane contains 6 of the points.

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Kummer variety

In mathematics, the Kummer variety of an abelian variety is its quotient by the map taking any element to its inverse.

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Linear system

A linear system is a mathematical model of a system based on the use of a linear operator.

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Nodal surface

In algebraic geometry, a nodal surface is a surface in (usually complex) projective space whose only singularities are nodes.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Tangent cone

In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities.

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Tetrahedroid

In algebraic geometry, a tetrahedroid (or tétraédroïde) is a special kind of Kummer surface studied by, with the property that the intersections with the faces of a fixed tetrahedron are given by two conics intersecting in four nodes.

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Theta divisor

In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally polarized) by the zero locus of the associated Riemann theta-function.

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Wave surface

In mathematics, Fresnel's wave surface, found by Augustin-Jean Fresnel in 1821, is a quartic surface describing the propagation of light in an optically biaxial crystal.

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Weddle surface

In algebraic geometry, a Weddle surface, introduced by, is a quartic surface in 3-dimensional projective space, given by the locus of vertices of the family of cones passing through 6 points in general position.

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Redirects here:

Gopel tetrad, Göpel tetrad, Kummer's surface, Rosenheim tetrad.

References

[1] https://en.wikipedia.org/wiki/Kummer_surface

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