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Catalogue Information
Field name	Details
Dewey Class	512.44
Title	Arithmetically Cohen-Macaulay Sets of Points in P 1 x P 1 ([EBook]) / by Elena Guardo, Adam Van Tuyl.
Author	Guardo, Elena
Added Personal Name	Van Tuyl, Adam author.
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2015.
Physical Details	VIII, 134 p. 25 illus. in color. : online resource.
Series	SpringerBriefs in Mathematics 2191-8198
ISBN	9783319241661
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-24166-1
Links to Related Works	Subject References: Algebraic Geometry . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Mathematics . Projective Geometry . Authors: Guardo, Elena . Van Tuyl, Adam . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 512.44 .

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

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