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| Schenck H. — Computational algebraic geometry |
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| Предметный указатель |
Affine space 2
Affine variety 2
Annihilator 7 12 82
Antipodal point 21
Artinian module 25 103
Artinian reduction 100
Artinian ring 25
Associated prime of ideal 8
Associated prime of module 11
Auslander — Buchsbaum theorem 148
Betti numbers (of resolution) 38
Betti numbers (of resolution) and Tor 114
Betti numbers (topological) 67
Bezier cubic 2
Bezout's theorem 20 23 31—32 37
Bilinear map 89
Boundary, of simplex 66
Buchberger algorithm 53
Canonical divisor 139
Castelnuovo-Mumford regularity see Regularity
Category 80
Catenary 146
Cauchy integral formula 179
Cauchy — Riemann equations 175—176
Cauchy's theorem 178
Cech complex 130
Chain complex 27
Chain homotopy 112
Chain, ascending 4
Chain, descending 25
CoCoa 174
Codimension of ideal 146
Codimension of projective variety 29
Coface 78
Cohen — Macaulay 149
Cohen — Macaulay and codimension 150
Cohen — Macaulay and Ext 152
Cohen — Macaulay and Stanley — Reisner ring 159
Cohen — Macaulay module 149
Cohen — Macaulay ring 149
Cohen — Macaulay, arithmetically 149
Cohomology, Cech 130—132 162
Cohomology, local 161—162
Cohomology, sheaf 129—132
Cohomology, simplicial 86
Commutative diagram 35 107
Complete intersection 32
Complete intersection, local 82—84
Complete intersection, resolution of 46—48
Complex number 175
Complex, cellular 72
Complex, chain 27
Complex, simplicial 66
Contravariant 80 116
Convex combination 2 73
Convex set 2
Coordinate ring 13 155
Covariant 80 112 116
Decomposition irreducible 6
Decomposition primary 6
Degree and Hilbert polynomial 29—31
Degree and hyperplane section 42—45
Degree of polynomial 22
Degree of projective variety 29—31
Degree, shifting 22
Dehn — Sommerville relations 76 158
Depth 147—148
Dimension and Hilbert polynomial 29—31
Dimension and hyperplane section 42—45
Dimension of graded piece  22
Dimension of module 147
Dimension of projective variety 29—31
Dimension of ring(Krull) 146
Dimension relation among definitions 147
Direct limit 168 127
Division algorithm 52
Divisor 133—143
Divisor and global sections 135
Divisor and locally free sheaf 134
Divisor, effective 141
Divisor, map associated to 135
Divisor, nonspecial 142
Divisor, very ample 135
Double complex 124
Eisenbud — Goto conjecture 158
Elimination ideal 60—61
Embedding 133
Euclidean algorithm 168 50
Euler characteristic 27 140
Euler relation 73
Exact sequence 27
Exact sequence and nonzerodivisor 42
Exact sequence of complexes 108
Exact sequence of sheaf cohomology 131
Exponent vector 51
Ext 116—123
Ext and associated primes 118 152
Ext and localization 152
Extension of modules 123
Extension of scalars 89
f-vector 73 158—161
Field 164
Free resolution 36—42
Free resolution and generic points 97—98
Free resolution and Hilbert series 41
Free resolution, finite 37
Free resolution, graded 37
Free resolution, infinite 40
Free resolution, minimal 40
functor 80
Functor, additive 112
Functor, contravariant 80 116
Functor, covariant 80 112
Functor, exact 81
Functor, left derived 111—112
Functor, left exact 85 116
Functor, right derived 116
Functor, right exact 90 112
Generic condition 33
Generic condition, hyperplane 29 31
Generic condition, points 97-98
Genus of curve 134 139 173
Genus of real surface 111
Genus of simplicial complex 111
Global section 128—132
Gotzmann's theorem 99
Graded lex order 51
Graded map 26
Graded module 22
Graded ring 21
Green's conjecture 143
Green's theorem 176—178
Grobner basis 53
Grobner basis and elimination 60—63
Grobner basis and modules 58—60
Grobner basis and syzygies 59—60
Group 163—164
Group homomorphism 164
Group, abelian 163
Group, normal subgroup 164
h-vector 73—76 159—160
Hilbert basis theorem 5
Hilbert function 22
Hilbert function and points 92—98
Hilbert function of polynomial ring 22
Hilbert function, growth of 99—106
Hilbert nullstellensatz 14
Hilbert polynomial 28—31
Hilbert polynomial and monomial ideal 55—57
Hilbert polynomial and resolution 41
| Hilbert polynomial and Riemann—Roch 140—141
Hilbert polynomial of points 29
Hilbert series 23
Hilbert series and resolution 41
Hilbert series of Artinian module 25
Hilbert series of polynomial ring 25
Hilbert syzygy theorem 37
Hilbert syzygy theorem, proof of 114
Hilbert — Burch theorem 150—152
Holomorphic 176
Hom 80 84—88
Hom, graded 88
Homogeneous coordinates 19
Homogeneous ideal 21
Homogeneous polynomial 20
Homology 27
Homology, long exact sequence 109
Homology, reduced 67
Homology, simplicial 67
Homomorphism group 164
Homomorphism module 166
Homomorphism ring 166
Homomorphism, sheaf 128
Horseshoe lemma 115
Hyperelliptic 143
Hypersurface 2
Ideal 165
Ideal of a set 3
Ideal, ascending chain of 4
Ideal, generators of 2
Ideal, initial 10
Ideal, intersection 4
Ideal, irreducible 167
Ideal, maximal 167
Ideal, membership 3
Ideal, monomial 10
Ideal, primary 167
Ideal, prime 167
Ideal, principal 167
Ideal, product of 4
Ideal, quotient 10
Ideal, radical 7 167
Ideal, sum of 4
Independent conditions 93
Integral domain 165
Jacobian ideal 82
Jacobian matrix 171
Jacobson radical 36
Klein bottle 71
Koszul complex 47 60 114
Krull dimension 146
Laurent series 181 134
Leray cover 131
Lexicographic order 51
Lexicographic order and projection 61—62
Line arrangement 82—84
Linear equivalence 135
Linear system, complete 143
Linear system, incomplete 155—156
Local duality 155 161
Local duality and Ext 155
localization 81—84
Macaulay 2
Macaulay 2 Commands, annihilator 120 121
Macaulay 2 Commands, apply 171 172
Macaulay 2 Commands, basis 93 137
Macaulay 2 Commands, betti 38—39
Macaulay 2 Commands, chainComplex 69
Macaulay 2 Commands, codim 30 150 172
Macaulay 2 Commands, coker 23 31
Macaulay 2 Commands, degree 31 172
Macaulay 2 Commands, degrees 170
Macaulay 2 Commands, differentials (dd) 38—39
Macaulay 2 Commands, equality (==) 9
Macaulay 2 Commands, Ext 117 119 155
Macaulay 2 Commands, factor 25
Macaulay 2 Commands, genericMatrix 57
Macaulay 2 Commands, gens 169 31
Macaulay 2 Commands, graded Lex order 54
Macaulay 2 Commands, grobner basis (gb) 54
Macaulay 2 Commands, hilbertFunction 23
Macaulay 2 Commands, hilbertPolynomial 30
Macaulay 2 Commands, homology (HH_i) 70
Macaulay 2 Commands, Horn 87
Macaulay 2 Commands, ideal 8
Macaulay 2 Commands, ideal quotient (I:J) 16
Macaulay 2 Commands, image 161
Macaulay 2 Commands, intersect 8
Macaulay 2 Commands, jacobian 83 172
Macaulay 2 Commands, kernel 169 154 172
Macaulay 2 Commands, Lex order 62
Macaulay 2 Commands, load 48—49 173
Macaulay 2 Commands, local cohomology (HH^i) 161
Macaulay 2 Commands, map 93 136 137 153
Macaulay 2 Commands, matrix 169 23
Macaulay 2 Commands, mingens 172
Macaulay 2 Commands, minors 57 138 151 172
Macaulay 2 Commands, MonomialOrder 54
Macaulay 2 Commands, pdim 150
Macaulay 2 Commands, pfaffians 143
Macaulay 2 Commands, poincare 24
Macaulay 2 Commands, primaryDecomposition 9 120
Macaulay 2 Commands, prune 87 88
Macaulay 2 Commands, radical 9
Macaulay 2 Commands, random 31 172
Macaulay 2 Commands, rank 70
Macaulay 2 Commands, res 38
Macaulay 2 Commands, ring 169
Macaulay 2 Commands, scan 171
Macaulay 2 Commands, source 170
Macaulay 2 Commands, submatrix 94
Macaulay 2 Commands, subquotient 87 88
Macaulay 2 Commands, target 170
Macaulay 2 Commands, tensor (**) 69 91
Macaulay 2 Commands, time 57
Macaulay 2 Commands, Tor 113 114
Macaulay 2 Commands, transpose 94
Macaulay 2 Commands, vars 94
Macaulay 2 Commands, while 171
Macaulay's theorem 99
Macaulay, commands 193
Macaulay, getting started 168—171
Manifold 134 111
Mapping cone 47
Mayer — Vietoris sequence 109—111
Meromorphic function 181 134—139
Module 165
Module, annihilator of 82
Module, Cohen—Macaulay 149
Module, finitely generated 165
Module, free 165 35
Module, graded 21 22
Module, homomorphism 166
Module, Noetherian 4
Module, projective 35
Monomial ideal 26
Monomial order 51
Monomial, initial 51
Motzkin's conjecture 158
Multiplicity 32—33 20
Nakayama's lemma 36
Node 173
Noetherian module 5
Noetherian ring 4
Nonzerodivisor 42
Nullstellensatz 14
One-form 139
Open set 13
Open set, distinguished 13
Orientation of simplicial complex 66
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