INDEX 157
integral
for
Pd
, 55
for a projective variety, 101
interpolation problem, 119, 127
inverse systems, 117, 127
invertible sheaf belonging to a divisor, 108
irregularity of a surface, 103
Jacobian
determinant, 43, 126
formula, 62
ideal, 70
ahler
different, 70
differential forms, 35
Koszul complex, 23
lattice, 130
lattice polytope, 131
Laurent
expansion of a differential, 107
series, 36
linear map induced by the residue, 40
Lipman, J., 86
local cohomology
at a point x, 1
and completion, 56
local duality theorem
for power series rings, 45
for complete reduced local rings, 94
on integral varieties, 95
local criterion of flatness, 75
Macaulay’s inverse systems, 117, 127
Matlis dual, 127
maximal Cohen-Macaulay module, 31
membership
problem, 123
in the radical of a complete intersection,
124
in zero-dimensional ideals, 124
midpoint, 99
minimal number of generators of the
canonical module, 68
Minkowski sum, 144
module of differentials, 35, 52
M -quasiregular sequence, 26
M -regular sequence, 26
multiplicative group, 131
multiplicity of a variety at a point, 96
Nagata’s conjecture, 127
Newton, 99
polytope, 144
Noether different, 70
Noether normalization, 81, 123
of an analytic algebra, 82
Noether position, 123
normal
lattice polytope, 132
fan of a polytope, 138
numerator of a generalized fraction, 32
permutation of (quasi-)regular sequences,
26
polyhedral cone, 130
polynomial solutions
of differential equations, 116
presentation as a complete intersection, 71
principal part of a Laurent series, 36
projective
closure, 63
toric variety, 132
punctured spectrum, 9
quantum cohomology ring, 119
quasicoherent sheaf, 8
quasiregular sequence, 26
quotient property of residues, 40
ramification index, locus, point, 109
rational differential form, 52
reducedness of zero-dimensional complete
intersections, 61
refinement of a covering, 19
regular differential forms, 84
at regular points, 84
at Cohen-Macaulay (Gorenstein) points,
86
at complete intersection points, 87
on the affine cone, 101
on toric varieties, 131, 137, 139
regular differentials in the sense of
Rosenlicht, 87
regular sequence, 26
Reiss relation, 64
relation
between the arithmetic and the
geometric genus, 103
between the
ˇ
Cech and the Koszul
complex, 29
between toric and local residues, 143
to residues on smooth curves, 96
representative of the ezoutian, 120
residual complex, 114
residue
at a closed point of a variety, 95
at a point x, 56
at a singular point of a curve, 107
at the vertex of the affine cone, 56, 101
for convergent power series, 46
for power series, 39
map, 39, 93
of an exact differential, 37
on smooth curves, 96
sum, 57
symbol, 39, 79, 115
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