Arithmetically Cohen Macaulay Sets Of Points In P 1 X P 1

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Arithmetically Cohen Macaulay Sets Of Points In P 1 X P 1

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Author : Elena Guardo
language : en
Publisher: Birkhäuser
Release Date : 2015-11-25

Arithmetically Cohen Macaulay Sets Of Points In P 1 X P 1 written by Elena Guardo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-25 with Mathematics categories.

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem. In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra. Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research. Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature.

Arithmetically Cohen Macaulay Sets Of Points In P1 9

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Author : Elena Guardo
language : en
Publisher:
Release Date : 2015

Arithmetically Cohen Macaulay Sets Of Points In P1 9 written by Elena Guardo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Commutative algebra categories.

Commutative Algebra Methods For Coding Theory

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Author : Ştefan Ovidiu I. Tohăneanu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-01

Commutative Algebra Methods For Coding Theory written by Ştefan Ovidiu I. Tohăneanu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.

This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90’s, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.

Hiroshima Mathematical Journal

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Author :
language : en
Publisher:
Release Date : 1994

Hiroshima Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2005

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The Geometry Of Schemes

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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

The Geometry Of Schemes written by David Eisenbud 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 2006-04-06 with Mathematics categories.

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Ideals Of Powers And Powers Of Ideals

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Author : Enrico Carlini
language : en
Publisher: Springer Nature
Release Date : 2020-05-21

Ideals Of Powers And Powers Of Ideals written by Enrico Carlini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Mathematics categories.

This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.

3264 And All That

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Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-14

3264 And All That written by David Eisenbud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-14 with Mathematics categories.

3264, the mathematical solution to a question concerning geometric figures.

Foundations Of Algebraic Geometry

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Author : André Weil
language : en
Publisher:
Release Date : 1946

Foundations Of Algebraic Geometry written by André Weil and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1946 with Geometry, Algebraic categories.

This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.

Enriques Surfaces I

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Author : F. Cossec
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Enriques Surfaces I written by F. Cossec 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 2012-12-06 with Mathematics categories.

This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approach the subject from a completely geometric point of view although heavily relying on algebraic methods. Some of the techniques presented in this book can be applied to the study of algebraic surfaces of other types. We hope that it will make this book of particular interest to a wider range of research mathematicians and graduate students. Acknowledgements. The undertaking of this project was made possible by the support of several institutions. Our mutual cooperation began at the University of Warwick and the Max Planck Institute of Mathematics in 1982/83. Most of the work in this volume was done during the visit of the first author at the University of Michigan in 1984-1986. The second author was supported during all these years by grants from the National Science Foundation.