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Vasconcelos W. — Integral Closure
Vasconcelos W. — Integral Closure

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Название: Integral Closure

Автор: Vasconcelos W.

Аннотация:

Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

This book is intended for graduate students and researchers in the fields mentioned above. It contains, besides exercises aimed at giving insights, numerous research problems motivated by the developments reported.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 519

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$F_0$ condition      25
$F_1$ condition      25
$G\infty$ condition      25
$hdeg_1$      142
$R_1$-ification      323
$S_2$-ification of a Rees algebra      116
$S_2$-ification, ideal      183
$S_2$-ification, Rees algebra      318
$S_2$-ification, ring      317
a-invariant      218
Abhyankar — Hartshorne lemma      316
Adjoint ideal      92
Algebra of linear type      413 453
Almost complete intersection      295
Almost complete intersection module      420
Almost complete intersection Rees algebra      461
Analytic deviation of a module      420
Analytic deviation of an ideal      52
Analytic independence      24
Analytic spread      45
Analytic spread of a module      160 229 416
Approximation complexes of an ideal      294
Approximation complexes, acyclicity      295
Arithmetic Cohen — Macaulayfication      210 221
Arithmetic degree      75
Arithmetic degree, hyperplane section      77
Arithmetic degree, rules of computation      76
Arithmetic Noether normalization      365
Associated graded module      132
Associated graded ring, filtration      7
Associated primes of filtrations      379
Asymptotic depth of an ideal      52
Auslander dual      153
Auslander — Buchsbaum equality      279
Bass numbers of a module, big deg      152
Bdeg, the optimal Deg      158
Betti numbers of a module, big deg      152
Betti numbers of symmetric algebras      298
Bidual, construction      482
Bidual, test      481
Big reduction number ofan ideal      75 201
Big reduction number, arithmetic degree      77
Big reduction number, Castelnuovo — Mumford regularity      82
Bigrank of a module      73
Blowing-up morphism      4
Blowup algebras      4
Bourbaki ideal      469
Bourbaki sequence      469
Bow tie of a graph      327
Briancon — Skoda bound      90
Briancon — Skoda number      404
Briancon — Skoda number of a ring      91
Briancon — Skoda number of an ideal      91
Buchsbaum module      143
Buchsbaum — Rim coefficients of a module      423
Buchsbaum — Rim multiplicity      422 423
Buchsbaum — Rim polynomial, algebra      475
Buchsbaum — Rim polynomial, module      474
Burch's formula      52
Canonical module of a Rees algebra      237
Canonical module of an algebra      237
Canonical module of an ideal      237
Canonical module of the expected form      255
Canonical module, $S_2$-ification      317
Canonical module, construction      318
Cascading reductions      116
Castelnuovo — Mumford regularity      130 218
Cayley — Hamilton polynomials      66
Cayley — Hamilton theorem      66
Cayley — Hamilton theorem, arithmetic degree      78
Cech complex      212
Chebyshev's inequality      389
Classical multiplicity      14 130
Classical multiplicity for modules      131
Co-type of an ideal      23
Coefficient ideal of a reduction      91
Cohen — Macaulay Rees algebra      477
Cohomological degree      140
Commuting variety of an algebra      413
Commuting variety, Lie algebra      453
Complete ideal      39
Complete integral closure      377
Complete intersection module      420 428
Complete intersection Rees algebra      457
Completeness test      44
Completeness test, monomial ideal      393
Computation of multiplicities      396
Condition $S_k$ of Serre      232
Conductor of an algebra      320
Conormal module      30
Conormal module, analytic spread      192
Conormal module, Rees algebra      191
Content of a polynomial      61
Content of an ideal      285
Contracted ideal      35
Core of an ideal      82 91
D-sequence      25
Dedekind — Mertens formula      61
Degree function      14 130
Degree of a prime ideal      313
Degrees and localization      152
Depth of a module      276
Derivations      377
Descending condition for integral subextensions      331
Determinant divisor of a module      439
Determinant of a module      71
Determinant of an endomorphism      70—72
Deviation of a module      420
Deviations of an ideal      52
Dimension of symmetric algebras      27
Divisor class group      246
Divisor class group, associated graded ring      254
Divisor in a ring      241
Divisor of a module      438
Divisor of the expected form      255
Divisorial degree of an ideal      331
Divisorial extension of a ring      330
Double Koszul complex      293
Dual basis and Gorenstein ideal      57
Edge ideal      326
Edge subring      326
Element integral over an ideal      33
Embedding degree of an algebra      349
Embedding dimension of an algebra      348
End divisor      239
Equimultiple ideal      51 64
Equimultiple module      420
Exceptional divisor      237
Expected form of the fundamental divisor      269
Explicit prolongation      253
Extended degree, Buchsbaum — Rim multiplicity      437
Extended degree, Castelnuovo — Mumford regularity      148
Extended degree, classical multiplicity      140
Extended prime      28
Fiber cone      45
Filter-regular sequence      229
Finiteness of the integral closure      314
Finiteness of the integral closure, graded algebra      315
Fitting ideal      25
Forster — Swan number      27
Fundamental divisor of the blowup algebra      238
Fundamental divisor of the expected form      261
Fundamental divisor, Veronese subrings      264
Gap in a divisor      257
Gaps in a graded module      257
Generalized multiplicity      136
Generating sequence of a module      257
Generic complete intersection ideal      485
Generic hyperplane section      144
Geometrically linked ideals      289
h-polynomial of a graded module      100
Hdeg, the homological degree      141
Height unmixed ideal      485
Hilbert coefficients      98 108
Hilbert coefficients of a graded module      100
Hilbert coefficients of a normal ideal      376
Hilbert filtration      64
Hilbert function      97
Hilbert polynomial of a module      100
Hilbert polynomial of an algebra      98
Hilbert polynomial of an ideal      106
Hilbert syzygy theorem      277
Hilbert — Kunz function for modules      428
Hilbert — Poincare series      97
Hironaka lemma      369
Homogeneous ideal      38
Homological degree      141
Hypersurface ring      312
Ideal module      419
Ideal of leading coefficients      314
Ideal of linear type      23
Ideal with sliding depth      291
Idealizer ring      307
Ideals of reduction number one      55
Index of nilpotency      47 121
Index of normalization      51
Inertial analytic spread of an ideal      53
Integral closure and primary components      449
Integral closure filtration      374
Integral closure of a module      416
Integral closure of a module, absolute closure      418
Integral closure of an ideal      33
Integral closure of an ideal, dimension one      47
Integral closure, completeness test for Integral closure, monomial ideals      393
Integral closure, construction for monomial ideals      393
Integral closure, membership test for monomial ideals      392
Integral closure, of an edge subring      327
Integral closure, Rees algebra approach      335
Integrally closed complete intersection      486
Integrally closed ideal      39
Integrally closed module      418
Intertwining module      83
Intertwining Rees algebra      83
Jacobian dual      22
Jacobian ideal of an algebra      320
Jacobian ideal of an ideal      485
Jacobian ideal, conductor      320
Jacobian normality criteria      323
Kahler differentials      466
Koszul complex      273
Koszul homology      271
Koszul homology, algebra      271
Koszul homology, annihilator      286
Koszul homology, canonical module      275
Koszul homology, codimension two ideal      278
Koszul homology, grade sensitivity      274
Koszul homology, module structure      280
Koszul homology, reduction      300
Koszul homology, rigidity      278
Koszul homology, symbolic powers      305
Koszul homology, top homology of reductions      301
Koszul homology, Tor      280
Koszul homology, vanishing      274
Krull — Serre normality criterion      316
Lech formula      129
Licci ideal      290
Linkage      289
Linked ideals      289
Local analytic spread      226
Local duality      214
M-complex      294
m-full closure      43
m-full ideal      42
m-full ideal, monomial ideal      385
m-full module      450
Macaulay Theorem      397
Matlis duality      214
McRae determinant      72
Membership oracle      393
Minimal polynomial of an endomorphism      70
Minimal reduction      45
Minimal reduction of an algebra      6
Minimal reduction of an ideal      45
Module of linear type      30 413
Module with a linear presentation      23
Module with rank one relations      440
Monomial ideal, integral closure      392
Monomial ideal, normalization of the Rees algebra      403
Monomial subrings, normalization      383
Monte Carlo method      389
Multiplicity and a-invariant      48
Multiplicity and Macaulay's theorem      397
Multiplicity and volume of polyhedra      387
Multiplicity function      136
Multiplicity of a graded algebra      98
Noether normalization      310
Noether normalization module      313
Noether normalization, graded algebra      313
Noether normalization, integral closure of ideals      487
Noether normalization, Jacobian ideal      321
Noether normalization, reductions      46
Norm of an element in an extension      71
Norm of an ideal      487
Normal determinantal ideal      40
Normal ideal      39
Normal module      418
Normal Rees algebra      457
Normality of algebras of linear type      453
Normalization in one step      321
Normalization index, equimultiple ideal      401
Normalization index, monomial ideal      403
Normalization of a blowup      44
Normalization of an edge subring      327
Normalization of an ideal      400
Normalization of an ideal, generation index      401
Normalization of an ideal, normalization index      400
Normalization of modules      473
Normally Cohen — Macaulay ideal      52
Normally torsionfree ideal      40
Normally torsionfree, edge ideal      326
Northcott ideal      61
Notion of genericity      140
Number of generators of an ideal, non-primary Cohen — Macaulay ideals      174
Number of generators of an ideal, primary ideals      169
Number of generators of an ideal, role of the socle      170
Number of generators, Cohen — Macaulay ideals      165
Order determinant of a module      439
Orientable module      439
Postulation number      98
Pro-polynomial function      49
Probabilistic approach to multiplicities      387
Prolongation of divisors      243 253
Proper operation      331
Proper sequence      296
Quasi-Gorenstein algebra      347
Quasi-Gorenstein ideal      283
Quasi-unmixed local ring      44
Rank of a module      67 413 439
Rank of the divisor class group      250
Ratliff — Rush closure of an ideal      113
Reduction module      103
Reduction number      32
Reduction number of a filtration      64 380
Reduction number of a module      229 416
Reduction number of an ideal      54
Reduction number, approximation      47
Reduction number, arithmetic degree      78
Reduction number, determinantal ideal      55
Reduction number, Grobner basis      80
Reduction number, initial ideal      48
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