Toroidal Embeddings, Part 1 |
Contents
Equivariant Embeddings of Tori | 1 |
SemiStable Reduction | 53 |
Toroidal Embeddings | 73 |
Copyright | |
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algebraic assume bijection birational Borel Borel subgroup canonical Cartier div Cartier divisor closed point closure Cohen-Macaulay coherent sheaf commutative components containing convex interpolation convex rational polyhedral coordinates Corollary corresponds formally definition denote embedding without self-intersection equation equivalent equivariant equivariant embedding exists f.r.p.p. decomposition face fact fibre finite type follows fractional ideals function f graph hence hyperplane integral closure integral structure invariant invertible sheaf irreducible Lemma Let f linear function linear subspace Moreover morphism non-singular normal variety notation open set open subset orbit PL(X polyhedron projective subdivision Proof prove rational polyhedral cone resp scheme semi-group semi-stable reduction sheaf of fractional simplex simplices singularities strata stratum subgroup T-invariant T-space Theorem toroidal embedding torus embedding vector vertexes vertices waterman point Weil divisor X₁ Y₁ Z C Star יח