156 INDEX
degree
of a generalized fraction, 42
of a zero-dimensional scheme, 96
of the socle, 60, 77
degree form, 58
δ-functor, 3, 11
denominator of a generalized fraction, 32
description of cohomology by generalized
fractions, 48
diameter, 99
of complete intersection curves, 99
of subschemes (cycles) in affine space, 99
differential
forms, 35, 52
operator, 115
differentiation
in the
ˇ
Cech complex, 11
in the Koszul complex, 22, 23
of differential forms, 35
differents and Jacobians, 72
direct image of a sheaf, 5
double complex, 14
double dual, 85
dual
of a lattice, 130
of a sheaf, 85
of a polyhedral cone, 130
duality theorem
for
Pd
, 55
for projective varieties, 102
dualizing
complex, 114
form, 119
module, 40, 65, 84
sheaf, 85
effective computation, 125
embedding the semigroup algebra into the
total coordinate ring, 134
endomorpphism ring of the canonical
module, 112
equality of generalized fractions, 32, 34
´ etale, 66
Euler
characteristic, 50
derivation, 100
sequence, 53
Euler-Cramer paradox, 62
Euler-Jacobi
formula, 62
vanishing condition, 122
toric generalization, 145, 147
Euler’s formula, 54
evaluation at the origin, 116
exact differentials, 37
exactness of the Koszul complex, 26
exchange lemma
for separating systems of parameters, 82
extension of a sheaf by zero, 2
extension rule for generalized fractions, 33
exterior
algebra, 22
differentiation, 52
Ext groups of sheaves, 110
facet normal, 134
field
of Laurent series, 36
of rational functions, 52
finiteness theorem for cohomology, 49
finite derivation, 35
Fitting ideal, 70
flasque
module, 1
resolution, 2
sheaf, 1
flasque sheaf associated to a sheaf, 2
form of maximal degree (degree form), 58
Frobenius
algebra, 77
map, 38
fundamental class of a variety, 86
generalized
ezoutian, 70
fraction, 32
Jacobian, 74
generator of the socle, 29
germ of a section, 1
geometric genus, 103
global
membership, 123
residue, 143
Gorenstein
algebra, 69
duality, 77, 78
ideal, 77, 116, 117
point, variety, 86
gradient, 63
Grothendieck residue symbol, 39
group of sections with support in Y , 1
Hilbert polynomial, 51
homogeneous cohomology class
generalized fraction, 41, 48
homogenization, 54
in a toric geometry, 135
ubl, R., 63
hyperplane at infinity, 63
incremental quotient, 119
injective
object, 1
OX -module, 2
R-module, 6
sheaf, 3
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