xx Notation DP Cartier divisor of a polytope or polyhedron (4,7) PD polyhedron of a torus-invariant divisor (4) XD toric variety of a basepoint free divisor (6) ΣD fan of XD (6) φ∗D pullback of a Cartier divisor (6) Support Functions ϕD support function of a Cartier divisor (4) ϕP support function of a polytope or polyhedron (4) SF(Σ) support functions for Σ (4) SF(Σ,N) support functions for Σ integral with respect to N (4) Sheaves Γ(U,F ) sections of a sheaf over an open set (4) F| U restriction of a sheaf to an open set (4) Fp stalk of a sheaf at a point (6) F ⊗O X G tensor product of sheaves of OX-modules (6) H omO X (F ,G ) sheaf of homomorphisms (6) F ∨ dual sheaf of F , equals H omO X (F ,OX) (6) f∗F direct image sheaf Specific Sheaves OX structure sheaf of a variety X (3) OX ∗ sheaf of invertible elements of OX (4) KX constant sheaf of rational functions for X irreducible (6) OX(D) sheaf of a Weil divisor D on X (4) IY ideal sheaf of a subvariety Y ⊆ X (3) M sheaf on Spec(R) of an R-module M (4) M sheaf on XΣ of the graded S-modules M (5) OX Σ (α) sheaf of the S-module S(α) (5) Vector Bundles and Locally Free Sheaves L , E invertible sheaf (line bundle) and locally free sheaf (6) π : V → X vector bundle (6) π : VL → X rank 1 vector bundle of an invertible sheaf L (6) f ∗ L pullback of an invertible sheaf (6) φL ,W map to projective space determined by W ⊆ Γ(X,L ) (6) P(V), P(E ) projective bundle of vector bundle or locally free sheaf (7) Σ × D fan for rank 1 vector bundle VL for L = OX Σ (D) (7)

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