Introduction to toric varieties

By: William FultonMaterial type: TextTextSeries: Annals of Mathematics Studies ; No. 131Publication details: New Jersey: Princeton University Press, [c1993]Description: 157 pISBN: 9780691000497LOC classification: QA571
Contents:
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
Summary: 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. --- summary provided by publisher
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Mathematic Rack No 6 QA571 (Browse shelf (Opens below)) Available Billno: 42677 ; Billdate: 25.02.2019 01793
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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

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. --- summary provided by publisher

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