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Eisenbud D. — Computations in Algebraic Geometry with Macaulay 2
Eisenbud D. — Computations in Algebraic Geometry with Macaulay 2

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Название: Computations in Algebraic Geometry with Macaulay 2

Автор: Eisenbud D.

Аннотация:

This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 345

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
#      49
# ?      50
$b^L_f (s)$      291
$D_{n+1}$      293
$in_{(u,v)} (L)$      287
$J^L(f^s )$, algorithm for      296
$R_n$ as a $D_n$-module      289
$y_1$-homogenization      295
$\Theta^r_k$      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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