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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1/ by Elena Guardo, Adam Van Tuyl.
作者:	Guardo, Elena.
其他作者:	Van Tuyl, Adam.
面頁冊數:	VIII, 134 p. 25 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Commutative algebra. -
電子資源:	https://doi.org/10.1007/978-3-319-24166-1
ISBN:	9783319241661

Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
Guardo, Elena.

Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1[electronic resource] /by Elena Guardo, Adam Van Tuyl. - 1st ed. 2015. - VIII, 134 p. 25 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

Introduction -- The Biprojective Space P^1 x P^1 -- Points in P^1 x P^1 -- Classification of ACM Sets of Points in P^1 x P^1 -- Homological Invariants -- Fat Points in P^1 x P^1 -- Double Points and Their Resolution -- Applications -- References.

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.

ISBN: 9783319241661

Standard No.: 10.1007/978-3-319-24166-1doiSubjects--Topical Terms:

672047
Commutative algebra.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
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520 $a 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.
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