The Hilbert Function Of A Level Algebra
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The Hilbert Function Of A Level Algebra
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Author : A. V. Geramita
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
The Hilbert Function Of A Level Algebra written by A. V. Geramita and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
The Hilbert Function Of A Level Algebra
DOWNLOAD
Author : A. V. Geramita
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
The Hilbert Function Of A Level Algebra written by A. V. Geramita and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
Syzygies And Hilbert Functions
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Author : Irena Peeva
language : en
Publisher: CRC Press
Release Date : 2007-03-20
Syzygies And Hilbert Functions written by Irena Peeva and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-20 with Mathematics categories.
Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts.
Deformation Of Artinian Algebras And Jordan Type
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Author : Anthony Iarrobino
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-06
Deformation Of Artinian Algebras And Jordan Type written by Anthony Iarrobino and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-06 with Mathematics categories.
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18?22, 2022, at the Universit‚ Grenoble Alpes, Grenoble, France. Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case. Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry.
Perspectives On Four Decades Of Algebraic Geometry Volume 1
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Author : Alberto Albano
language : en
Publisher: Springer Nature
Release Date : 2025-01-22
Perspectives On Four Decades Of Algebraic Geometry Volume 1 written by Alberto Albano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-22 with Mathematics categories.
The first of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research. With chapters written by established leaders in the field as well as younger researchers, readers will gain a wide-ranging perspective of the area. The volume also commemorates the significant talent and contributions of Alberto Collino, whose scientific accomplishments helped shape the themes and topics covered. Perspectives on Four Decades of Algebraic Geometry, Volume 1 will be a valuable resource for those interested in the ways algebraic geometry has expanded over the years and continues to grow. "Quadratic Counts of Twisted Cubics" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
A Celebration Of Algebraic Geometry
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Author : Brendan Hassett
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-09-11
A Celebration Of Algebraic Geometry written by Brendan Hassett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-11 with Mathematics categories.
This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Commutative Algebra
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Author : Irena Peeva
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-01
Commutative Algebra written by Irena Peeva and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-01 with Mathematics categories.
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.
Commutative Algebra And Its Interactions To Algebraic Geometry
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Author : Nguyen Tu CUONG
language : en
Publisher: Springer
Release Date : 2018-08-02
Commutative Algebra And Its Interactions To Algebraic Geometry written by Nguyen Tu CUONG and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Mathematics categories.
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.
Newton S Method Applied To Two Quadratic Equations In Mathbb C 2 Viewed As A Global Dynamical System
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Author : John H. Hubbard
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Newton S Method Applied To Two Quadratic Equations In Mathbb C 2 Viewed As A Global Dynamical System written by John H. Hubbard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things: The Russakovksi-Shiffman measure does not change the points of indeterminancy. The lines joining pairs of roots are invariant, and the Julia set of the restriction of $N$ to such a line has under appropriate circumstances an invariant manifold, which shares features of a stable manifold and a center manifold. The main part of the article concerns the behavior of $N$ at infinity. To compactify $\mathbb{C}^2$ in such a way that $N$ extends to the compactification, the authors must take the projective limit of an infinite sequence of blow-ups. The simultaneous presence of points of indeterminancy and of critical curves forces the authors to define a new kind of blow-up: the Farey blow-up. This construction is studied in its own right in chapter 4, where they show among others that the real oriented blow-up of the Farey blow-up has a topological structure reminiscent of the invariant tori of the KAM theorem. They also show that the cohomology, completed under the intersection inner product, is naturally isomorphic to the classical Sobolev space of functions with square-integrable derivatives. In chapter 5 the authors apply these results to the mapping $N$ in a particular case, which they generalize in chapter 6 to the intersection of any two conics.
Hardy Spaces And Potential Theory On C 1 Domains In Riemannian Manifolds
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Author : Martin Dindoš
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Hardy Spaces And Potential Theory On C 1 Domains In Riemannian Manifolds written by Martin Dindoš and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The author studies Hardy spaces on C1 and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors.