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
ezoutian, 72, 120
generalized, 70
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
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