Arithmetically Cohen-Macaulay sets of points in P¹ × P¹ /

Arithmetically Cohen-Macaulay sets of points in P¹ × P¹ /

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Bibliographic Details
Author / Creator:	Guardo, Elena, author.
Imprint:	Cham : Springer, [2015] ©2015
Description:	1 online resource.
Language:	English
Series:	SpringerBriefs in mathematics SpringerBriefs in mathematics.
Subject:	Mathematics. Geometry, Algebraic. Commutative algebra. Commutative rings. Geometry, Projective. Commutative algebra. Commutative rings. Geometry, Algebraic. Geometry, Projective. Mathematics.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11096637

Hidden Bibliographic Details
Other authors / contributors:	Van Tuyl, Adam, author.
ISBN:	9783319241661 3319241664 9783319241647 3319241648 9783319241647
Notes:	Includes bibliographical references and index. Vendor-supplied metadata.
Summary:	This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P̂1 x P̂1. 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 P̂1 x P̂1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P̂1 x P̂1, 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 P̂1 x P̂1 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.
Other form:	Print version: Guardo, Elena. Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1. Cham : Springer International Publishing, ©2015 9783319241647
Standard no.:	10.1007/978-3-319-24166-1

Description
Summary:	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.
Physical Description:	1 online resource.
Bibliography:	Includes bibliographical references and index.
ISBN:	9783319241661 3319241664 9783319241647 3319241648