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Cover: 9780691000497 | Introduction to Toric Varieties. (AM-131), Volume 131 | William Fulton
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Introduction to Toric Varieties. (AM-131), Volume 131
Taschenbuch von William Fulton
Sprache: Englisch

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Beschreibung
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 quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.
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 quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.
Über den Autor
William Fulton is Professor of Mathematics at the University of Chicago.
Inhaltsverzeichnis
Ch. 1Definitions and examples
Details
Erscheinungsjahr: 1993
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 172
ISBN-13: 9780691000497
ISBN-10: 0691000492
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Fulton, William
Hersteller: Princeton University Press
Maße: 234 x 156 x 10 mm
Von/Mit: William Fulton
Erscheinungsdatum: 01.08.1993
Gewicht: 0,272 kg
preigu-id: 123698195
Über den Autor
William Fulton is Professor of Mathematics at the University of Chicago.
Inhaltsverzeichnis
Ch. 1Definitions and examples
Details
Erscheinungsjahr: 1993
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 172
ISBN-13: 9780691000497
ISBN-10: 0691000492
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Fulton, William
Hersteller: Princeton University Press
Maße: 234 x 156 x 10 mm
Von/Mit: William Fulton
Erscheinungsdatum: 01.08.1993
Gewicht: 0,272 kg
preigu-id: 123698195
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