Index

abelian sheaf, 1

action of the torus on an aﬃne toric

variety, 131

acyclic object for a δ-functor, 3

aﬃne

cone, 47, 101

morphism, 20

residue theorem, 58

toric variety, 131

analytic presentation

as a complete intersection, 72

Apollonius of Perga, 99

applications

of residues and duality, 106–109, 112–127

of residues in combinatorics, 46

of the residue theorem, 61–64, 96–99

of toric residues, 146–148

approach of Scheja-Storch, 79

arithmetic genus, 51

for integral curves, 51

associated sheaf, 1

augmented algebra, 74

base change, 65, 75

B´ ezoutian, 72, 120

generalized, 70

B´ ezout’s formula, 97

canonical

divisor, 109

flasque resolution, 2

sheaf, 84

trace, 65

trace of differential forms, 87, 88

canonical homomorphism

from

ˇ

Cech to sheaf cohomology, 13

from local to global cohomology, 4

canonical module, 40, 65, 84

of an ideal, 77, 116, 117

of a (local) algebra, 84

Cartier

divisor, 108

operator, 39

ˇ

Cech cohomology

cochain, cocycle, coboundary, 11

ˇ

Cech complex

alternating, normalized, 11

sheafified, 12

under refinement, 19

ˇ

Cech resolution, 12

centroid (center of mass), 96

character, 131

Chow group, 134

classical formulas of combinatorics, 46

Cohen-Macaulay

point, variety, 86

type, 68

cohomology

algebra, 119

of the direct image, 20

of the punctured spectrum, 10

with support in Y , 1

with values in a sheaf, 1

complementary module, 66

and completion, 67

complete duality, 46, 111

complete intersection

algebra, 71

ideal, 115

subscheme, 61

complexity, 124, 125

conductor, 67

degree, 113

cone of a lattice polytope, 131

constant coeﬃcient differential operator,

115

constant sheaf, 1

Cousin complex, 114

criterion of Serre for aﬃneness, 8

critical degree, 138

curvature of algebraic curves and

hypersurfaces, 64

Dedekind complementary module

different, 66

Dedekind’s formula for the conductor and

the different, 67

155