A01=William Fulton
Addition
Affine space
Affine variety
Alexander duality
Alexander Grothendieck
Algebraic curve
Atiyah-Singer index theorem
Author_William Fulton
Automorphism
Betti number
Big O notation
Category=PBF
Category=PBM
Codimension
Cohomology
Commutative property
Complete intersection
Convex polytope
Dedekind sum
Dimension
Dimension (vector space)
Discrete valuation ring
Divisor
Divisor (algebraic geometry)
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Equivalence class
Equivariant K-theory
Euler characteristic
Explicit formula
Fundamental group
Graded ring
Grassmannian
H-vector
Hirzebruch surface
Hodge theory
Homomorphism
Intersection theory
Invertible sheaf
Isoperimetric inequality
Lattice (group)
Leray spectral sequence
Limit point
Line bundle
Line segment
Linear subspace
Mathematical induction
Moduli space
Moment map
Monotonic function
Natural number
Open set
Picard group
Pick's theorem
Polytope
Projective space
Quadric
Quotient space (topology)
Regular sequence
Resolution of singularities
Riemann-Roch theorem
Serre duality
Simplicial complex
Spectral sequence
Subgroup
Subset
Summation
Surjective function
Tangent bundle
Topology
Toric variety
Unit disk
Weil conjecture
Zariski topology
Product details
- ISBN 9780691000497
- Weight: 227g
- Dimensions: 197 x 254mm
- Publication Date: 01 Aug 1993
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
William Fulton is Professor of Mathematics at the University of Chicago.
