The Hilbert Function Of A Level Algebra PDF Download
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| Author | : A. V. Geramita |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821839403 |
Download The Hilbert Function of a Level Algebra Book in PDF, ePub and Kindle
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.
| Author | : Maria Evelina Rossi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 115 |
| Release | : 2010-08-25 |
| Genre | : Mathematics |
| ISBN | : 3642142400 |
Download Hilbert Functions of Filtered Modules Book in PDF, ePub and Kindle
Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one place many new developments of this theory by using a unifying approach which gives self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular in the theory of the Hilbert Functions and related topics.
| Author | : Irena Peeva |
| Publisher | : CRC Press |
| Total Pages | : 305 |
| Release | : 2007-03-20 |
| Genre | : Mathematics |
| ISBN | : 1420050915 |
Download Syzygies and Hilbert Functions Book in PDF, ePub and Kindle
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.
| Author | : Jim Agler |
| Publisher | : American Mathematical Society |
| Total Pages | : 330 |
| Release | : 2023-02-22 |
| Genre | : Mathematics |
| ISBN | : 1470468557 |
Download Pick Interpolation and Hilbert Function Spaces Book in PDF, ePub and Kindle
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
| Author | : Valeria D'Orazio |
| Publisher | : |
| Total Pages | : |
| Release | : 2014 |
| Genre | : Electronic dissertations |
| ISBN | : |
Download On Unimodality of Hilbert Functions of Artinian Level Algebras of Codimension 3 and Type 2 and 3 Book in PDF, ePub and Kindle
We prove the unimodality of the Hilbert Function for some classes of codimension three graded algebras of Cohen-Macaulay types 2 and 3. The method of proof uses the explicit structure theorems similar to the structure theorems for Gorenstein algebras in codimension 3. Using the structure of the resolution, we write the Hilbert function explicitly and thus calculate the h-vector and verify it is indeed unimodal.
| Author | : Ciro Ciliberto |
| Publisher | : Walter de Gruyter |
| Total Pages | : 401 |
| Release | : 2008-08-22 |
| Genre | : Mathematics |
| ISBN | : 311019970X |
Download Projective Varieties with Unexpected Properties Book in PDF, ePub and Kindle
This volume contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Also included are research papers that grew out of discussions among the participants and their collaborators. All the papers are research papers, but some of them also contain expository sections which aim to update the state of the art on the classical subject of special projective varieties and their applications and new trends like phylogenetic algebraic geometry. The topic of secant varieties and the classification of defective varieties is central and ubiquitous in this volume. Besides the intrinsic interest of the subject, it turns out that it is also relevant in other fields of mathematics like expressions of polynomials as sums of powers, polynomial interpolation, rank tensor computations, Bayesian networks, algebraic statistics and number theory.
| Author | : Irena Peeva |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 705 |
| Release | : 2013-02-01 |
| Genre | : Mathematics |
| ISBN | : 1461452929 |
Download Commutative Algebra Book in PDF, ePub and Kindle
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.
| Author | : Alexander J. Schaefer |
| Publisher | : |
| Total Pages | : 90 |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
Download Level Algebras Book in PDF, ePub and Kindle
| Author | : David Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 784 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461253500 |
Download Commutative Algebra Book in PDF, ePub and Kindle
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
| Author | : Dolors Herbera |
| Publisher | : Birkhäuser |
| Total Pages | : 180 |
| Release | : 2016-11-30 |
| Genre | : Mathematics |
| ISBN | : 3319454412 |
Download Extended Abstracts Spring 2015 Book in PDF, ePub and Kindle
This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.
