Power Sums Gorenstein Algebras And Determinantal Loci

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Power Sums, Gorenstein Algebras, and Determinantal Loci

Anthony Iarrobino,Vassil Kanev
Power Sums Gorenstein Algebras and Determinantal Loci Book PDF

Author : Anthony Iarrobino,Vassil Kanev
Publisher : Springer
Page : 365 pages
File Size : 43,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540467076

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Power Sums, Gorenstein Algebras, and Determinantal Loci by Anthony Iarrobino,Vassil Kanev Pdf

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.

Power Sums, Gorenstein Algebras, and Determinantal Loci

Anthony Iarrobino,Vassil Kanev
Power Sums Gorenstein Algebras and Determinantal Loci Book PDF

Author : Anthony Iarrobino,Vassil Kanev
Publisher : Springer
Page : 354 pages
File Size : 55,7 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 3662214865

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Power Sums, Gorenstein Algebras, and Determinantal Loci by Anthony Iarrobino,Vassil Kanev Pdf

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.

Commutative Algebra and its Interactions to Algebraic Geometry

Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG
Commutative Algebra and its Interactions to Algebraic Geometry Book PDF

Author : Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG
Publisher : Springer
Page : 258 pages
File Size : 43,9 Mb
Release : 2018-08-02
Category : Mathematics
ISBN : 9783319755656

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Commutative Algebra and its Interactions to Algebraic Geometry by Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG Pdf

This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.

Decomposability of Tensors

Luca Chiantini
Decomposability of Tensors Book PDF

Author : Luca Chiantini
Publisher : MDPI
Page : 161 pages
File Size : 52,8 Mb
Release : 2019-02-15
Category : Mathematics
ISBN : 9783038975908

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Decomposability of Tensors by Luca Chiantini Pdf

This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics

The Hilbert Function of a Level Algebra

A. V. Geramita,Tadahito Harima,Juan C. Migliore,Yong Su Shin
The Hilbert Function of a Level Algebra Book PDF

Author : A. V. Geramita,Tadahito Harima,Juan C. Migliore,Yong Su Shin
Publisher : American Mathematical Soc.
Page : 139 pages
File Size : 47,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839409

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The Hilbert Function of a Level Algebra by A. V. Geramita,Tadahito Harima,Juan C. Migliore,Yong Su Shin Pdf

Let $R$ be a polynomial ring over an algebraically closed field and let $A$ be a standard graded Cohen-Macaulay quotient of $R$. The authors state that $A$ is a level algebra if the last module in the minimal free resolution of $A$ (as $R$-module) is of the form $R(-s)a$, where $s$ and $a$ are positive integers. When $a=1$ these are also known as Gorenstein algebras. The basic question addressed in this paper is: What can be the Hilbert Function of a level algebra? The authors consider the question in several particular cases, e.g., when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. The authors give new methods for showing that certain functions are NOT possible as the Hilbert function of a level algebra and also give new methods to construct level algebras. In a (rather long) appendix, the authors apply their results to give complete lists of all possible Hilbert functions in the case that the codimension of $A = 3$, $s$ is small and $a$ takes on certain fixed values.

Advances in Algebra and Geometry

C. Musili
Advances in Algebra and Geometry Book PDF

Author : C. Musili
Publisher : Springer
Page : 311 pages
File Size : 42,8 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9789386279125

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Advances in Algebra and Geometry by C. Musili Pdf

Contributed articles presented at the Conference, sponsored by National Science Foundation, USA [and others].

Gorenstein Dimensions

Lars W. Christensen
Gorenstein Dimensions Book PDF

Author : Lars W. Christensen
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 40,9 Mb
Release : 2000-11-06
Category : Mathematics
ISBN : 3540411321

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Gorenstein Dimensions by Lars W. Christensen Pdf

This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content. Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.

Commutative Algebra and Its Connections to Geometry

Alberto Corso,Claudia Polini
Commutative Algebra and Its Connections to Geometry Book PDF

Author : Alberto Corso,Claudia Polini
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 51,5 Mb
Release : 2011-10-20
Category : Mathematics
ISBN : 9780821849590

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Commutative Algebra and Its Connections to Geometry by Alberto Corso,Claudia Polini Pdf

This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil. The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.

Commutative Algebra

Irena Peeva
Commutative Algebra Book PDF

Author : Irena Peeva
Publisher : Springer Science & Business Media
Page : 705 pages
File Size : 52,6 Mb
Release : 2013-02-01
Category : Mathematics
ISBN : 9781461452928

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Commutative Algebra by Irena Peeva Pdf

This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Connections Between Algebra, Combinatorics, and Geometry

Susan M. Cooper,Sean Sather-Wagstaff
Connections Between Algebra Combinatorics and Geometry Book PDF

Author : Susan M. Cooper,Sean Sather-Wagstaff
Publisher : Springer
Page : 328 pages
File Size : 50,8 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9781493906260

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Connections Between Algebra, Combinatorics, and Geometry by Susan M. Cooper,Sean Sather-Wagstaff Pdf

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Geometry and Complexity Theory

J. M. Landsberg
Geometry and Complexity Theory Book PDF

Author : J. M. Landsberg
Publisher : Cambridge University Press
Page : 353 pages
File Size : 41,9 Mb
Release : 2017-09-28
Category : Computers
ISBN : 9781107199231

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Geometry and Complexity Theory by J. M. Landsberg Pdf

This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.

Algebraic Geometry and Geometric Modeling

Mohamed Elkadi,Bernard Mourrain,Ragni Piene
Algebraic Geometry and Geometric Modeling Book PDF

Author : Mohamed Elkadi,Bernard Mourrain,Ragni Piene
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 44,6 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 9783540332756

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Algebraic Geometry and Geometric Modeling by Mohamed Elkadi,Bernard Mourrain,Ragni Piene Pdf

This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.

On the Shape of a Pure O-sequence

Mats Boij
On the Shape of a Pure O sequence Book PDF

Author : Mats Boij
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 40,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869109

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On the Shape of a Pure O-sequence by Mats Boij Pdf

A monomial order ideal is a finite collection $X$ of (monic) monomials such that, whenever $M\in X$ and $N$ divides $M$, then $N\in X$. Hence $X$ is a poset, where the partial order is given by divisibility. If all, say $t$, maximal monomials of $X$ have the same degree, then $X$ is pure (of type $t$). A pure $O$-sequence is the vector, $\underline{h}=(h_0=1,h_1,...,h_e)$, counting the monomials of $X$ in each degree. Equivalently, pure $O$-sequences can be characterized as the $f$-vectors of pure multicomplexes, or, in the language of commutative algebra, as the $h$-vectors of monomial Artinian level algebras. Pure $O$-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their $f$-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure $O$-sequences.

Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order

Yorck Sommerhäuser
Yetter Drinfel d Hopf Algebras over Groups of Prime Order Book PDF

Author : Yorck Sommerhäuser
Publisher : Springer
Page : 164 pages
File Size : 44,8 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540454236

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Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order by Yorck Sommerhäuser Pdf

Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.

The Lefschetz Properties

Tadahito Harima,Toshiaki Maeno,Hideaki Morita,Yasuhide Numata,Akihito Wachi,Junzo Watanabe
The Lefschetz Properties Book PDF

Author : Tadahito Harima,Toshiaki Maeno,Hideaki Morita,Yasuhide Numata,Akihito Wachi,Junzo Watanabe
Publisher : Springer
Page : 268 pages
File Size : 45,5 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9783642382062

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The Lefschetz Properties by Tadahito Harima,Toshiaki Maeno,Hideaki Morita,Yasuhide Numata,Akihito Wachi,Junzo Watanabe Pdf

This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.