Iarrobino A., Kanev V. — Power Sums, Gorenstein Algebras, and Determinantal Loci :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Iarrobino A., Kanev V. — Power Sums, Gorenstein Algebras, and Determinantal Loci

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Power Sums, Gorenstein Algebras, and Determinantal Loci

Авторы: Iarrobino A., Kanev V.

Аннотация:

This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 345

Добавлена в каталог: 20.11.2009

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

Предметный указатель

Primitive ideal of a singularity      101
Principal system      8
Punctual = 0-dimensional      xx
Punctual Hilbert scheme      see Hilbert scheme
Quadratic form      18
Rational normal curve      54 215
Rational normal curve, points on, as annihilating scheme      217
Regularity      see Castelnuovo - Mumford regularity
Saturated ideal      46
Saturation      47 298
Saturation degree      48
Scheme, generic      221
Scheme, limit      144
Scheme, nonsmoothable      221
Scheme, smoothable      145
Schemes, flat family of      142
Self-associated point set      214-220
Self-associated point set, as annihilating scheme      217
Self-associated point set, ideal of      215
Serre's criterion      82
Small tangent space to parameter space of compressed algebras      221 224 230
Smoothable scheme      145
Socle degree      67
Strong Lefschetz property      109 111
Sum of powers      see Power sum
Sylvester's theorem      27
Tangent space to       42 73 79 96 97 249
Tangent space to , and square of Gorenstein ideal      79
Tangent space to , annihilating scheme      10
Tangent space to , when annihilating scheme is a self-associated point set      217

Tangent space to , when annihilating scheme is compressed      222
Tangent space to $\mathbb{P}Gor(T)$       96
Tangent space to determinantal locus of catalecticant      73 113
Tangent space to determinantal locus of catalecticant, reducible locus      79
Tangent space to the punctual Hilbert scheme      79 97 249
Tangent space, small, to parameter space of compressed algebras      221
Terracini's Lemma      xiii 58
Tight annihilating scheme      135
Tight subscheme of higher dimension Gorenstein scheme      202
Unimodal      see Gorenstein sequence unimodal
Vanishing ideal at points of $\mathbb{P}^{2}$ , having no DP-form for which it defines a tight annihilator scheme      98
Vanishing ideal at points of $\mathbb{P}^{2}$ , square of      100
Vanishing ideal at points of $\mathbb{P}^{2}$ , square of, and symbolic square      103
Vanishing ideal at points of $\mathbb{P}^{r - 1}$       14
Vanishing ideal at points of $\mathbb{P}^{r - 1}$ , and Gorenstein ideal      14
Vanishing ideal at points of $\mathbb{P}^{r - 1}$ , square of      104
Vanishing ideal at points of $\mathbb{P}^{r - 1}$ , square of, and Gorenstein ideal      84
Vanishing ideal, square of, at points of $\mathbb{P}^{4}$ on RNC      314
Vanishing, at points, square of      43 100 235
Vanishing, at points, square of, for $\mathbb{P}^{2}$       101
Vanishing, at points, square of, for $\mathbb{P}^{r - 1}$       104
Vanishing, at points, symbolic square square      101
Veronese variety      10 16
Veronese variety, and minors of catalecticants      21
Veronese variety, chordal variety of      20
Veronese variety, generation of ideal of      21
Veronese variety, multisecant variety of      39 245- 247
Veronese variety, rational normal curve      39
Veronese variety, Terracini's Lemma      58
Waring's problem for forms      xiii xix 40 57-62

1 2

О проекте