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Herzog B. — Kodaira-Spencer Maps in Local Algebra
Herzog B. — Kodaira-Spencer Maps in Local Algebra

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Название: Kodaira-Spencer Maps in Local Algebra

Автор: Herzog B.

Аннотация:

The monograph contributes to Lech's inequality - a 30-year-old problem of commutative algebra, originating in the work of Serre and Nagata, that relates the Hilbert function of the total space of an algebraic or analytic deformation germ to the Hilbert function of the parameter space.
A weakened version of Lech's inequality is proved using a construction that can be considered as a local analog of the Kodaira-Spencer map known from the deformation theory of compact complex manifolds. The methods are quite elementary, and will be of interest for researchers in deformation theory, local singularities and Hilbert functions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 176

Добавлена в каталог: 15.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$F_A$-filtration      9
$F_A$-minimal      62
$F_A$-minimal, with respect to (b, d)      62
$\overline{F}$-distinguished basis      59
Algebra generators, homogeneous      115
Artin — Rees filtration      10
Associated graded ring      2
Base change      145
Base change homomorphism      145
Basic exact sequence      42
Closure      14
Cofinite      3
Compatible filtrations      9
complete      13
Completion      13
Contained in a filtration      4
Critical      163
Definable over a subalgebra      111
Defined over a subalgebra linear map      111
Defined over a subalgebra module      111
Defining equations of the deformation space      153
Defining equations of the fibre      150
Defining exact sequence for $F_{M^\land}^{d}$      14
Defining exact sequence for cl(N)      14
Defining exact sequence for in(I)      9
Defining ideal      103
Defining submodule      111
Deformation      x
Deformation, embedded germ      145
Deformation, germ      ix
Deformation, space, defining equations      153
Deformations, embedded of first order      157
Deformations, functor of embedded      157
Degree      1
Degreewise lexicographic order      148
Derivations      103
Direct image filtration      7 9
Distinguished basis      59
Embedded deformation functor      157
Embedded deformation germ      145
Embedded deformations      157
Embedded first order deformations      157
Embedded Kodaira — Spencer map      106
Embedding of a permissible graded homomorphism      106
Exact sequence associated with a family      33
Exact sequence, basic      42
Exact sequence, defining for $F^{d}_{M^\land}$      14
Exact sequence, defining for cl(N)      14
Exact sequence, defining for in(I)      9
Exponential Hilbert series      133
F-distinguished basis      59
Family associated exact sequence      33
Family generating a filtration      7
Family of structure constants      118
Filtered module      8
Filtered module homomorphism      8
Filtered ring      2
Filtration      2 8
Filtration, contained in another one      4
Filtration, direct image of      7 9
Filtration, generated by a family      7
Filtration, ideal-adic      3 10
Filtration, induced on a factor ring      7
Filtration, induced on a subring      6
Filtration, inverse image of      6 9
Filtration, minimal      62
Filtration, q-adic      4
Filtration, quasi-homogeneous      4
Filtration, weight      4
Finite Hilbert function      76
Flatifying, filtration      91
Flatifying, prefiltration      91
Formal degree      163
Generating a filtration      7
Graded module      1
Graded module, homomorphism      2
Graded module, with finite Hilbert function      76
Graded ring      1
Graded ring, homomorphism      2
Graduationally flat      x
Hausdorff      3
Hilbert scheme      143
Hilbert series exponential      133
Hilbert series of a filtered ring      76
Hilbert series of a graded module      76
Hilbert series of a homomorphism      77
Hilbert — Samuel series of a filtered ring      77
Hilbert — Samuel series of a graded module      76
Hilbert — Samuel series of a homomorphism      77
Homogeneous      1
Homogeneous, algebra generators      115
Homogeneous, syzygy      31
Homomorphism of embedded deformation germs      145
Homomorphism of filtered modules      8
Homomorphism of filtered rings      3
Homomorphism of the associated graded rings      3
I-adic filtration      3 10
Ideal      9
Ideal-adic filtration of a module      10
Ideal-adic filtration of a ring      3
Image filtration      6 9
Inclusion of filtrations      4
Induced      6 7
Induced filtration on a factor ring      7
Induced filtration on a subring      6
Initial element      9
Initial form      9 148
Intersection of filtrations      4
Inverse image      9
Irrelevant entry      163
Irrelevant ideal      1
Kodaira — Spencer map      108
Kodaira — Spencer map, embedded      106
Krull dimension      77
Lech's problem      78
Liftable to a syzygy      31
Local singularity      x
Minimal      115 116
Minimal, flatifying prefiltration      93
Minimal, over a filtration      62
Minimal, w.r.t. a distinguished basis      62
Module filtration      8
Monomial lift      118
Monomial module generators      116
Multiplicity      77
Natural filtration      3
Natural topology      3
Nice distinguished basis      117
Non-standard degree      151
Normal module      103
Normally flat      101
Order degreewise lexicographic      148
Order in a filtered module      9
Order in a filtered ring      2
Order total      76
Permissible graded algebra      101
Permissible graded homomorphism      101
Permissible graded homomorphism, embedding of      106
Point functor      143
Prefiltration      39
q-adic filtration      4
Quasi-homogeneous filtration      4
refinement      14 21
Residually rational      xvi
Residually separable      xvi
Ring filtration      2
Russian conjecture      141
Schlessinger's $T^1$      103
Separated      3
Shifting degrees      2
Special fibre x      7
Standard basis      30
Standart monomial      148
Strict homomorphism      32
Strict system of generators      30
Stronger      21
Structure constants      66 117 150
Sum of filtrations      5
Sum transform      76 77
Syzygy      31
Tangent space      157 158
Tangentially flat x      3
Total order      76
Underlying lifts      117
Underlying system of algebra generators      117
Underlying system of module generators      117
Underlying vector space basis      117
Universal germ      147
Weaker      21
Weakly graded      102
Weight filtration      4
Zariski tangent space      157 158
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