Introduction to Toric Varieties pdf epub mobi txt 電子書下載2025

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出版者:Princeton University Press

作者:William Fulton

出品人:

頁數:180

译者:

出版時間:1993-7-12

價格:USD 57.50

裝幀:Paperback

isbn號碼:9780691000497

叢書系列:

圖書標籤:

數學
代數幾何
幾何
Mathematics
Algebraic_Geometry
algebraic-geometry
Geometry
計算機科學

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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 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.