GLOSSARY OF NOTATION xiii

Aσ semigroup algebra of σ 130

χm

character associated to m ∈ M 130, 131

Vσ aﬃne toric variety corresponding to σ 131

ω the d-form

dt1

t1

···

dtd

td

or the

(d + 1)-form

dt0

t0

···

dtd

td

131, 132

Int

σ∨

interior of

σ∨

131

C(∆) cone associated to a lattice polytope ∆ 131

S∆ semigroup algebra of a lattice polytope ∆ 132

L∆ quotient field of S∆ 132

I∆ dualizing ideal corresponding to ∆ 132

Resf toric residue (first and second versions) 133

uρ minimal generator of ρ ∩ N 133

Dρ divisor associated to minimal generator ρ 133

S total coordinate ring of the toric variety 133

div(χm) divisor of the character χm 134

Cl(X) group of torus-invariant Weil divisors

modulo linear equivalence 134

∆d standard d-simplex 134

β0 sum of the degrees of the variables 135

δ the critical degreee

∑d

i=0

deg Fi − β0 138

ResF toric residue (homogeneous versions) 138, 140

Σ∆ normal fan of ∆ 138

Resf global residue 144

∆(f) Newton polytope of a Laurent series f 144

∆F

σ

polynomial of toric residue ±1 148