Introduction to Toric Varieties. (AM-131), Volume 131 / / William Fulton.
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 geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Ri...
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Fulton, William, author. aut http://id.loc.gov/vocabulary/relators/aut Introduction to Toric Varieties. (AM-131), Volume 131 / William Fulton. Princeton, NJ : Princeton University Press, [2016] ©1993 1 online resource (180 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 131 Frontmatter -- Contents -- Preface -- Errata -- Chapter 1. Definitions and examples -- Chapter 2. Singularities and compactness -- Chapter 3. Orbits, topology, and line bundles -- Chapter 4. Moment maps and the tangent bundle -- Chapter 5. Intersection theory -- Notes -- References -- Index of Notation -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are "ed without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Toric varieties. MATHEMATICS / Geometry / Algebraic. bisacsh Addition. Affine plane. Affine space. Affine variety. Alexander Grothendieck. Alexander duality. Algebraic curve. Algebraic group. Atiyah-Singer index theorem. Automorphism. Betti number. Big O notation. Characteristic class. Chern class. Chow group. Codimension. Cohomology. Combinatorics. Commutative property. Complete intersection. Convex polytope. Convex set. Coprime integers. Cotangent space. Dedekind sum. Dimension (vector space). Dimension. Direct proof. Discrete valuation ring. Discrete valuation. Disjoint union. Divisor (algebraic geometry). Divisor. Dual basis. Dual space. Equation. Equivalence class. Equivariant K-theory. Euler characteristic. Exact sequence. Explicit formula. Facet (geometry). Fundamental group. Graded ring. Grassmannian. H-vector. Hirzebruch surface. Hodge theory. Homogeneous coordinates. Homomorphism. Hypersurface. Intersection theory. Invertible matrix. Invertible sheaf. Isoperimetric inequality. Lattice (group). Leray spectral sequence. Limit point. Line bundle. Line segment. Linear subspace. Local ring. Mathematical induction. Mixed volume. Moduli space. Moment map. Monotonic function. Natural number. Newton polygon. Open set. Picard group. Pick's theorem. Polytope. Projective space. Quadric. Quotient space (topology). Regular sequence. Relative interior. Resolution of singularities. Restriction (mathematics). Resultant. Riemann-Roch theorem. Serre duality. Sign (mathematics). Simplex. Simplicial complex. Simultaneous equations. Spectral sequence. Subgroup. Subset. Summation. Surjective function. Tangent bundle. Theorem. Topology. Toric variety. Unit disk. Vector space. Weil conjecture. Zariski topology. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691000497 https://doi.org/10.1515/9781400882526 https://www.degruyter.com/isbn/9781400882526 Cover https://www.degruyter.com/document/cover/isbn/9781400882526/original |
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Fulton, William, Fulton, William, |
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Fulton, William, Fulton, William, Introduction to Toric Varieties. (AM-131), Volume 131 / Annals of Mathematics Studies ; Frontmatter -- Contents -- Preface -- Errata -- Chapter 1. Definitions and examples -- Chapter 2. Singularities and compactness -- Chapter 3. Orbits, topology, and line bundles -- Chapter 4. Moment maps and the tangent bundle -- Chapter 5. Intersection theory -- Notes -- References -- Index of Notation -- Index |
author_facet |
Fulton, William, Fulton, William, |
author_variant |
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VerfasserIn VerfasserIn |
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Fulton, William, |
title |
Introduction to Toric Varieties. (AM-131), Volume 131 / |
title_full |
Introduction to Toric Varieties. (AM-131), Volume 131 / William Fulton. |
title_fullStr |
Introduction to Toric Varieties. (AM-131), Volume 131 / William Fulton. |
title_full_unstemmed |
Introduction to Toric Varieties. (AM-131), Volume 131 / William Fulton. |
title_auth |
Introduction to Toric Varieties. (AM-131), Volume 131 / |
title_alt |
Frontmatter -- Contents -- Preface -- Errata -- Chapter 1. Definitions and examples -- Chapter 2. Singularities and compactness -- Chapter 3. Orbits, topology, and line bundles -- Chapter 4. Moment maps and the tangent bundle -- Chapter 5. Intersection theory -- Notes -- References -- Index of Notation -- Index |
title_new |
Introduction to Toric Varieties. (AM-131), Volume 131 / |
title_sort |
introduction to toric varieties. (am-131), volume 131 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (180 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- Errata -- Chapter 1. Definitions and examples -- Chapter 2. Singularities and compactness -- Chapter 3. Orbits, topology, and line bundles -- Chapter 4. Moment maps and the tangent bundle -- Chapter 5. Intersection theory -- Notes -- References -- Index of Notation -- Index |
isbn |
9781400882526 9783110494914 9783110442496 9780691000497 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA571 |
callnumber-sort |
QA 3571 |
url |
https://doi.org/10.1515/9781400882526 https://www.degruyter.com/isbn/9781400882526 https://www.degruyter.com/document/cover/isbn/9781400882526/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516.3/53 |
dewey-sort |
3516.3 253 |
dewey-raw |
516.3/53 |
dewey-search |
516.3/53 |
doi_str_mv |
10.1515/9781400882526 |
oclc_num |
979747116 |
work_keys_str_mv |
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hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Introduction to Toric Varieties. (AM-131), Volume 131 / |
container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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