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| Eisenbud D. — Computations in Algebraic Geometry with Macaulay 2 |
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| Предметный указатель |
# 49
# ? 50
 291
 293
 287
 , algorithm for 296
 as a  -module 289
 -homogenization 295
 304
% 6 19
(u, v)-Groebner basis 287
-> 44
. 50
32749 17
:= 44
== 4
=> 49
Abelian surface 244
Absolutely irreducible 30
action 289 293
Action (of a differential operator) 286 288 290 291
Adjunction theory 29
Alexander dual 79
APPEND 43
apply 45
Arrays 42
Artinian see also ideal
Artinian, zero-dimensional 102
Assert 137
Backtracking algorithm 188
Basis reduction 180
Baues graph 182
Baues problem 191
Beilinson monad 215 237
Beilinson monad, applications of 241
Beilinson monad, differentials of 237
Bernstein (Bernstein — Sato) polynomial 291
Bernstein filtration 289
Bernstein inequality 289
Bernstein operator 291
Bernstein polynomial, algorithm for 297
Bernstein root 291
Bernstein — Gel’fand — Gel’fand correspondence 215 218
Betti 22
betti diagram 22
Betti number 162
Bezout number 101 122 127
Bezout’s Theorem 27 63 101 111 117
BGG 215
Bidegree 176
Bigraded ring of cohomology operators 177
Bilinear form 122
Bilinear form, signature 108 124
Bilinear form, symmetric 108
Bistellar flip 191
Blow-up 64 65
Borel 89
Borel-fixed 89
Bounded filtration 142
break 46
Brill — Noether number 253
Bundle, Horrocks — Mumford 244
Bundle, normalized 231
Bundle, self-dual 231
Bundle, Serre duality 231
Bundle, Serre’s criterion 227
Bundle, stable 231
Bundles of differentials 227
Calabi — Yau, 3-folds 267
Canonical bundle 26 32
Canonical curve 263
Canonical embedding 31 32
Cartan map 140
Cartan resolution 218
Castelnuovo — Mumford regularity 219
Cech complex 282
Chain complex 21
Chain property 95
Chow form 217
Classical adjoint 57
Clifford index 31 263
Coble self-dual sets of points 263
Code 52 155
Codimension 19
Cohen — Macaulay 63
Coherent component 200
Coherent sheaf, representation of 18
Cohomological dimension 282
Cohomology, intermediate 227
Cohomology, sheaf 26 222 224 225
Coker 21
Cokernel 21
Complete intersection 116 131
COMPLEX 21
Complex, differentials in 21
complexity 165 174
Computable field 284
Conic bundle 241
Conic bundle, elliptic 241
Conormal sequence 24
Contravariant cohomology module 157
Cotangent bundle 20 24 26
Cotangent sequence 20
Covariant cohomology module 157
Cover 81
Critical degree 165
Cubic scroll 66
Cubic space curve 18
Curve, general 31
Curve, hyperelliptic 31
Curve, plane quintic 32
Curve, trigonal 32
Cylinder 112
D-modules 288
Data types 41
DD 21 134
dd_i, i-th differential of a complex 22
Decompose 30
decompose a variety 30
Degree of a projective variety 19
DEGREES 22
Determinantal variety 66 111
Diagram, Betti 22
Differential operators 264
Differentials of a complex 21
Dimension (of a D-module) 289
Dimension of a projective variety 19
Discriminant 59 113
Distraction 92
Divided powers algebra 139
Division command 25
Divisor at infinity 200
Dn -modules 286
DO 45
Dual 79
Dual, Alexander 79
Duality 26
Duality of sheaves 226
Dualizing sheaf 26
Eliminant 104–106 114
Elimination theory 57 66 104
Ellipsoid 124
Elliptic curve 58
Embedded point 62 64
endl 47
Enumerative geometry 102—104 110 112 114
Enumerative geometry, real 107 118
Enumerative problem 103 112 115 121
Enumerative problem, fully real 117 119
Ext 32 131 155
| Ext-generator series 149
Exterior algebra 139 215
f-saturated 294
f-torsion free 294
f-vector 75
Factor 50
Fano scheme 68
Field, algebraically closed 101 113
Field, splitting 104
Files 46
Finite fields, use of 17
Flat limit 62 68
Flip graph 186
Flip search algorithm 188
for 45
Fourier — Motzkin elimination 188 206
Functions 44
Generates 135
Generators 19
Generic initial ideal 90 92
Generic monomial ideal 96
gens 19
Genus of a curve 30
get 47
Gonality 31
Graded Artinian Gorenstein ring 264
Graded Bass number 169
Graded Bass series 169
Graded Betti number 161
Graded complete intersection 131
Graded Poincare series 162
Grassmannian 69 112 113 115 127
Grassmannian local coordinates 117
Grassmannian not a complete intersection 116
Graver basis 182
Graver degree 183
Graver fiber 183
Green’s conjecture 32 263
Groebner basis 74 104
Groebner basis, reduced 116
Groebner basis, universal 182
Groebner cone 188
Groebner fan 199
H 245
Hartshorne — Rao module 256
Hash table 49
hessian 59
hh 26
Hilbert basis 203
Hilbert function 116
Hilbert scheme 91 251
Hilbert scheme, incidence graph 91
Hilbert series 75
hilbertSeries 162 169
Holonomic module 289
Homogeneous coordinate ring 18
Homogeneous derivation 139
Homogeneous ideal 18
Homological degree 176
Homological methods, introduction to 17
Homology 151
Homotopy continuation 110
homotopy, Bezout 111
homotopy, Groebner 111 117
homotopy, optimal 111
Horrocks — Mumford bundle 244
Hyperboloid 124
Hyperelliptic curve 31
Ideal 19
Ideal of minors 82
Ideal, A-graded 97 179
Ideal, Borel-fixed 89
Ideal, codimension 81
Ideal, coherent 185
Ideal, degree 102 103
Ideal, generic initial 90 92
Ideal, graph 81
Ideal, initial 74
Ideal, monomial 73 74
Ideal, permutahedron 86
Ideal, primary 77
Ideal, radical 102 104 120
Ideal, Stanley — Reisner 75
Ideal, toric 87
Ideal, torus isomorphism 185
Ideal, tree 80
Ideal, zero-dimensional 102 119 123
if 45
Image 21
Infinitesimal deformations 271
Initial form 287
Initial ideal 74 87
Initial ideal, square-free 111 117
Input 47
Integer programming 86 197
Internal degree 176
Intersection multiplicities 26
Intersection theory 26 101
Irreducible decomposition 30
Irreducible, absolutely 30
isBorel 89
isMonomialIdeal 75
Jacobian 24
Jacobian matrix 24
Join 43
Kernel of a module map 20
Kernel of a ring map 18 104
Keys of a hash table 49
Killing cohomology 232
Koszul map 140
Koszul-regular 146
Lawrence lifting 183
Lefschetz Theorem 283
Leibniz rule 139 286
Length of a module 27
Lie algebra 58
Lift to characteristic zero 277
Linear free resolution 219
LISTS 42
Lists, appending 43
Lists, joining 43
Lists, prepending 44
Load 47
Local cohomological dimension 282
Local cohomology 282
Local cohomology, algorithm for 305 310
Local cohomology, iterated 310
Localization, algorithm for 300
Lyubeznik numbers 312
Map of modules 25
Map of rings 18
Matrix 18
Matrix factorization 133
Matrix, unimodular 191
Maximal rank 256
method 52
Minimal test set 197
Minors 19
minPres.m2 211
Mirror families 277
Modules, how to represent 20
Moduli space 251
Moduli space of curves 253
Monad 230
Monad, Beilinson 215 236 237
Monad, display of 233
Monad, homology of 230
Monad, self-dual 234
Monad, type of 230
Monads, applications of 230
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