Power Sums, Gorenstein Algebras, and Determinantal Loci

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Power Sums, Gorenstein Algebras, and Determinantal Loci / Anthony Iarrobino, Anthony Iarrobino, Vassil Kanev, S. L. Kleiman

資料種別:

電子ブック

出版情報:

SpringerLink Books - AutoHoldings
Springer Berlin Heidelberg, 1999

著者名:

ISBN:

9783540667667 [3540667660]
9783540467076 [3540467076]

書誌ID:

OB00502139

子書誌情報

フルテキスト

所蔵情報

書誌詳細

その他の標題:

POWER SUMS, GORENSTEIN ALGEBRAS, & DETERMINANTAL LOCI

言語:

英語

目次情報:

Introduction: Informal History and Brief Outline

Canonical forms, and catalecticant matrices of higher partial derivatives of a form / 0.1：

Apolarity and Artinian Gorenstein algebras / 0.2：

Families of sets of points / 0.3：

Brief summary of chapters / 0.4：

Catalecticant Varieties / Part I：

Forms and Catalecticant Matrices / Chapter 1：

Apolarity and catalecticant varieties: the dimensions of the vector spaces of higher partials / 1.1：

Determinantal loci of the first catalecticant, the Jacobian / 1.2：

Binary forms and Hankel matrices / 1.3：

Detailed summary and preparatory results / 1.4：

Sums of Powers of Linear Forms, and Gorenstein Algebras / Chapter 2：

Waring's problem for general forms / 2.1：

Uniqueness of additive decompositions / 2.2：

The Gorenstein algebra of a homogeneous polynomial / 2.3：

Tangent Spaces to Catalecticant Schemes / Chapter 3：

The tangent space to the scheme Gor(T) parametrizing forms with fixed dimensions of the partials / 3.1：

The Locus PS(s,j;r) of Sums of Powers, and Determinantal Loci of Catalecticant Matrices / Chapter 4：

The case r = 3 / 4.1：

Gorenstein ideals whose lowest degree generators are a complete intersection / 4.2：

The smoothness and dimension of the scheme Gor(T) when r = 3: a survey / 4.4：

Catalecticant Varieties and the Punctual Hilbert Scheme / Part II：

Forms and Zero-Dimensional Schemes I: Basic Results, and the Case r = 3 / Chapter 5：

Flat families of zero-dimensional schemes and limit ideals / 5.1：

Existence theorems for annihilating schemes when r = 3 / 5.3：

The generator and relation strata of the variety Gor(T) parametrizing Gorenstein algebras / 5.3.1：

The morphism from Gor(T): the case T ? D(s,s,s) / 5.3.2：

Morphism: the case T ? D(s - a,s,s,s - a) / 5.3.3：

Morphism: the case T ? D(s - a,s,s - a) / 5.3.4：

Adimension formula for the variety Gor(T) / 5.3.5：

Power sum representations in three and more variables / 5.4：

Betti strata of the punctual Hilbert scheme / 5.5：

The length of a form, and the closure of the locus PS(s,j;3) of power sums / 5.6：

Forms and Zero-Dimensional Schemes, II: Annihilating Schemes and Reducible Gor(T) / 5.7：

Uniqueness of the annihilating scheme; closure of PS(s,J;r) / 6.1：

Varieties Gor(T), T = T(j,r), with several components / 6.2：

Other reducible varieties Gor(T) / 6.3：

Locally Gorenstein annihilating schemes / 6.4：

Multisecant varieties of the Veronese variety / Chapter 7：

Closures of the Variety Gor(T), and the Parameter Space G(T) of Graded Algebras / Chapter 8：

Questions and Problems / Chapter 9：

Divided Power Rings and Polynomial Rings / Appendix A：

Height Three Gorenstein Ideals / Appendix B：

Pfaffian formulas / B.1：

Resolutions of height 3 Gorenstein ideals andtheir squares / B.2：

Resolutions of annihilating ideals of power sums / B.3：

Maximum Betti numbers, given T / B.4：

The Gotzmann Theorems and the Hilbert Scheme (Anthony Iarrobino and Steven L. Kleiman) / Appendix C：

Order sequences and Macaulay's Theorem on Hilbert functions / C.1：

Macaulay and Gotzmann polynomials / C.2：

Gotzmann's Persistence Theorem and m-Regularity / C.3：

Examples of "Macaulay" Scripts / C.4：

Concordance with the 1996 Version / Appendix E：

References

Index

Index of Names

Index of Notation

Introduction: Informal History and Brief Outline

Canonical forms, and catalecticant matrices of higher partial derivatives of a form / 0.1：

Apolarity and Artinian Gorenstein algebras / 0.2：

Families of sets of points / 0.3：

Brief summary of chapters / 0.4：

Catalecticant Varieties / Part I：

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