Introduction to Toric Varieties
By (author) William Fulton
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Introduction to Toric Varieties by William Fulton
Book DescriptionToric 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.
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Book DetailsISBN: 9780691000497
(229mm x 152mm x 11mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 12-Jul-1993
Country of Publication: United States
Books By Author William Fulton
Free Ideal Rings and Localization in General Rings, Hardback (June 2006)
This book presents the theory of free ideal rings (firs) in detail.
Regional City, Hardback (January 2001)
A study of the regional city, explaining how regional-scale planning and design can help direct growth and reverse current trends in land use. The authors present their view of the policies and design principles required for metropolitan areas to transform themselves into regional cities.
Young Tableaux, Paperback (December 1996)» View all books by William Fulton
Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.
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