• Corpus ID: 29080159

Introduction to toric varieties

@inproceedings{Brasselet2004IntroductionTT,
  title={Introduction to toric varieties},
  author={Jean-Paul Brasselet},
  year={2004}
}
The course given during the School and Workshop “The Geometry and Topology of Singularities”, 8-26 January 2007, Cuernavaca, Mexico is based on a previous course given during the 23o Coloquio Brasileiro de Matematica (Rio de Janeiro, July 2001). It is an elementary introduction to the theory of toric varieties. This introduction does not pretend to originality but to provide examples and motivation for the study of toric varieties. The theory of toric varieties plays a prominent role in various… 
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We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and
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As my contribution to these proceedings, I will discuss the geometric invariant theory quotients of toric varieties. Specifically, I will show that quotients of the same problem with respect to
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Ju n 19 95 Residues in Toric Varieties June 22 , 1995
Introduction Toric residues provide a tool for the study of certain homogeneous ideals of the homogeneous coordinate ring of a toric variety—such as those appearing in the description of the Hodge
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References

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Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic
Topological methods in algebraic geometry
Introduction Chapter 1: Preparatory material 1. Multiplicative sequences 2. Sheaves 3. Fibre bundles 4. Characteristic classes Chapter 2: The cobordism ring 5. Pontrjagin numbers 6. The ring
THE GEOMETRY OF TORIC VARIETIES
ContentsIntroductionChapter I. Affine toric varieties § 1. Cones, lattices, and semigroups § 2. The definition of an affine toric variety § 3. Properties of toric varieties § 4. Differential forms on
Picard Groups of compact toric Varieties and combinatorial Classes of Fans
We consider the question what can be said about the rank of the Picard group Pic Xσ of a compact toric variety Xσ if we know only the combinatorial type of the associated fan σ. We establish upper
The Topology of Torus Actions on Symplectic Manifolds
This is an extended second edition of "The Topology of Torus Actions on Symplectic Manifolds" published in this series in 1991. The material and references have been updated. Symplectic manifolds and
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SummaryLetP be a simpled-polytope ind-dimensional euclidean space $$\mathbb{E}^d $$ , and let Π(P) be the subalgebra of the polytope algebra Π generated by the classes of summands ofP. It is shown
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Let P be a simplicial convex d-polytope with fi = fi(P) faces of dimension i. The vector f(P) = (f. , fi ,..., fdel) is called the f-vector of P. In 1971 McMullen [6; 7, p. 1791 conjectured that a
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For convex d-polytope P let ft{P) equal the number of faces of P of dimension i, 0 < i < d 1. f(P) = (f0(P)9 . . . , fd^QP)) is called the f vector of P An important combinatorial problem is the
Using Algebraic Geometry
Introduction.- Solving Polynomial Equations.- Resultants.- Computation in Local Rings.- Modules.- Free Resolutions.- Polytopes, Resultants, and Equations.- Integer Programming, Combinatorics, and
Eventails et varietes toriques
© Séminaire sur les singularités des surfaces (École Polytechnique), 1976-1977, tous droits réservés. L’accès aux archives du séminaire sur les singularités des surfaces implique l’accord avec les
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