Introduction to Toric Varieties. (AM-131), Volume 131 / / William Fulton

• Autore: Fulton William
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1993
• Descrizione fisica: 1 online resource (171 pages) : illustrations
• Disciplina: 516.3/53
• Soggetto topico: Toric varieties
• Soggetto non controllato: 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
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Introduction to Toric Varieties. (AM-131), Volume 131
• ISBN: 1-4008-8252-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154749903321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 131.; William H. Roever lectures in geometry.