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Schenck H. — Computational algebraic geometry
Schenck H. — Computational algebraic geometry

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Название: Computational algebraic geometry

Автор: Schenck H.

Аннотация:

Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 193

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $M_i$      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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