xii GLOSSARY OF NOTATION
τtx
linear form associated to the ezoutian 72
dx
t
generalized Jacobian 74
ωV/k sheaf of regular differential forms
(also called canonical or dualizing sheaf) 84
Reg V set of regular points of V 84
cV/k fundamental class of a variety 85
F ∗, F ∗∗ dual (double dual) of a sheaf F 85
Pic V Picard group of a variety V 86
CV/W complementary module of a
finite morphism V W 87
µx(X) multiplicity of X at x 96
∆(X) centroid of a zero-dimensional affine scheme 96
pg(V ) geometric genus of a projective variety 103
Coh(V ) category of coherent sheaves on V 110
δF i i-duality isomorphism 111
Sing(X) singular locus of X 112
δ(X) singularity degree of X 113
c(X) conductor degree of X 113
|µ| µ0 + ··· + µd, µ = (µ0, . . . , µd) Nd+1 115
µ! µ0! ··· µd!, µ = (µ0, . . . , µd) Nd+1 115
∂µ
(

∂X0
)µ0
··· (

∂Xd
)µd
, µ = (µ0, . . . , µd)
Nd+1
115

X0
µ0
··· Xd
µd
, µ = (µ0, . . . , µd)
Nd+1
116
PF (∂) differential operator associated
to F = {F0, . . . , Fd} 115
ev0 evaluation at zero 116
polysol(I(∂)) polynomial solutions of the differential equations
associated to an ideal I 116
P(V ) projective space associated to a vector space V 117
X(∆) toric variety associated to a lattice polytope 119
∆f (X, Z) representative of ezoutian of f = {f1, . . . , fd} 120
degX f degree of f in a set of variables X 123
(f) radical of the ideal (f) 127
Ω0 homogeneous d-form used for residues 128, 136
T the torus of Pk
d
or a toric variety 129, 131
Gm multiplicative group 129
G Ω0
F0 ··· Fd
homogeneous generalized fraction 129, 138
N, M dual lattices 130
σ∨
dual of a convex cone σ 130
σ(1) set of 1-dimensional faces of σ 130
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