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

GUARDO, Elena - Personal Name; TUYL, Adam Van - Personal Name;

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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Series Title: SpringerBriefs in Mathematics
Call Number: 512.5 GUA a
Publisher: Cham, Switzerland : Springer Cham., 2015
Collation: VIII, 134
Language: English
ISBN/ISSN: 978-3-319-24166-1
Classification: 512.5
Content Type: text
Media Type: computer
Carrier Type: online resource
Edition: Ed. 1
Subject(s): Algebraic Geometry
Commutative Rings and Algebras
Projective Geometry
Specific Detail Info: -
Statement of Responsibility: Elena Guardo, Adam Van Tuyl

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Cataloger: umi
Source: https://link.springer.com/book/10.1007/978-3-319-24166-1
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