Notation xxiii Equivariant Cohomology for a Torus Action Sym Z (M) symmetric algebra of M over Z (12) Sym Q (M) rational symmetric algebra on M, equals Sym Z (M) ⊗Z Q (12) s isomorphism s : Sym Q (M) (ΛT )Q (12) [D]T equivariant cohomology class of a T-invariant divisor D (12) X eq equivariant integral X eq : H•(X,Q) T → (ΛT )Q (13) H•(X,Q) T completion ∞ k=0 Hk(X,Q) T of equivariant cohomology of X (13) Λ completion of the equivariant cohomology of a point (13) Chow Groups and the Chow Ring Ak(X) Chow group of k-cycles modulo rational equivalence (12) Ak(X) cycles of codimension k modulo rational equivalence (12) A•(X) integral Chow ring of X smooth and complete (12) A•(X)Q rational Chow ring of X quasismooth and complete (12) Intersection Cohomology IH p i (X) ith intersection homology of X for perversity p (12) IHi(X) ith intersection cohomology of X for middle perversity (12) IHi(X)Q ith rational intersection cohomology of X (12) Cohomology Ring of a Complete Simplicial Toric Variety I Stanley-Reisner ideal of the fan Σ, ideal in Q[x1,...,xr] (12) J ideal ∑ r i=1 m,ui xi | m ∈ M⊆ Q[x1,...,xr] (12) RQ(Σ) Jurkiewicz-Danilov ring Q[x1,...,xr]/(I + J ) H•(XΣ,Q) (12) SRQ(Σ) Stanley-Reisner ring Q[x1,...,xr]/I H•(XΣ,Q) T (12) Hirzebruch-Riemann-Roch ci(E ) ith Chern class of a locally free sheaf E (13) ch(L ) Chern character of a line bundle L (13) Td(X) Todd class of the variety X (13) Bk kth Bernoulli number (13) ci = ci(TX) ith Chern class of the tangent bundle (13) Ti ith Todd polynomial in the ci (13) K(X) Grothendieck group of classes of coherent sheaves on X (13) χT(L ) equivariant Euler characteristic (13) χσ(L T ) local contribution of σ ∈ Σ(n) to χT(L ) (13) chT(L ) equivariant Chern character of L (13) TdT(X) equivariant Todd class of X (13) Todd(x) formal Todd differential operator for the variable x (13)

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