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＜図書＞Introduction to toric varieties

責任表示 by William Fulton Annals of mathematics studies ; no. 131 図書 Princeton, N.J. : Princeton University Press 1993 英語 xi, 157 p. : ill., port. ; 25 cm 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 ge...metry 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. 続きを見る http://hdl.handle.net/2324/1905966

所蔵情報

: pbk 理系図1F 開架 003212007002867 411.8/F 86 1993
: pbk 理系図1F 開架 031212010000482 411.8/F 86 1993

書誌詳細

一般注記 "This monograph is an elaboration of a series of lectures delivered by William Fulton at the 1989 William H. Roever Lectures in Geometry, held on June 5-10 at Washington University, St Louis, Missouri"--Facing t.pIncludes bibliographical references (p. 149) and indexes LCSH:Toric varieties LCC:QA571DC20:516.3/53NDC8:411.8 1000030804 0691033323 BA20878601 ISBN:0691033323 ; PRICE:\$32.50: pbk ; ISBN:0691000492 ; PRICE:\$16.95 2009.09.10 2009.11.02