158 INDEX
residue formula
for the multiplicity, 96
for centroids, 97
residue theorem
affine version, 58
for
Pd
, 57
for projective varieties, 104
for projective curves, 107
residues and duality for proper varieties,
106
restriction property of residues, 40
retraction, 74
Riemann-Hurwitz genus formula, 109
right-derived functor, 1
ringed space, 1
scheme at infinity, 63
section of a sheaf, 1
semigroup algebra, 130
of a lattice polytope, 132
separable Noether normalization, 81
of analytic algebras, 82
in the graded case, 100
separated scheme, 16
separating system of parameters, 82
Serre’s finiteness conditions, 49
sheaf
associated to a module, 1, 47
of differential forms, 52
of rational d-forms, 52
of regular d-forms, 84
of Zariski d-forms, 86
simplicial toric variety, 143
singularity degree, 113
skyscraper sheaf, 9
socle
degree, 60, 77, 117
of a zero-dimensional local or graded
ring, 29
standard
covering of
Pd
k
, 57
d-simplex, 134
scalar product, 63
trace, 65
strict complete intersection, 119
support
of a divisor, 108
of a section, 1
T -acyclic object, 3
tangent, 63
tangent hyperplane, 61
tangential center, 99
Tate trace, 73
theorem of
ezout, 97
Cayley-Bacharach, 62
Chasles, 99
G. Humbert, 64
Pappus, 62
Pascal, 62
Reiss, 64
Riemann-Roch for projective curves, 108
toric
affine variety, 131
Euler-Jacobi vanishing theorem, 145, 147
homogeneous coordinates, 133
projective variety, 132
quotient property, 148
residue, 133, 138, 140
residues and resultants, 149
transformation law, 140
torsion of differential forms, 86
torus, 129
torus-invariant Weil divisor, 133
total
complex of a double complex, 14
coordinate ring, 133
ramification number, 109
sum of residues, 124
trace
map of an algebra, 65
of an endomorphism, 65
trace formula
for residues, 93, 95, 104
of Hasse, 96
transformation law for residues, 40
transition determinant, 26
transitive law
for the complementary module and the
different, 67
for dualizing sheaves, 88
for the trace, 65
transitive properties of regular differential
forms, 87, 106
transversal intersection, 61
universal
derivation, 35, 52
module of differentials, 35
universally finite
derivation, 35
module of differentials, 35
vertex of the affine cone, 47, 101
very ample sheaf, 49
volume polynomial, 119
Waring’s problem, 127
Weierstraß preparation theorem, 91
weighted case, 61, 121
Zariski differentials, 86
zero-dimensional complete intersection, 58
Previous Page Next Page