The Resource Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)
Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)
Resource Information
The item Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This brief presents a solution to the interpolation problem for arithmetically CohenMacaulay (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 selfcontained, 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
 Language
 eng
 Extent
 1 online resource.
 Contents

 1 Introduction
 2 The biprojective space P1 x P1
 3 Points in P1 x P1
 4 Classification of ACM sets of points in P1 x P1
 5 Homological invariants
 6 Fat points in P1 x P1
 7 Double points and their resolution
 8 Applications
 References
 Index
 Isbn
 9783319241647
 Label
 Arithmetically CohenMacaulay sets of points in P1 × P1
 Title
 Arithmetically CohenMacaulay sets of points in P1 × P1
 Statement of responsibility
 Elena Guardo, Adam Van Tuyl
 Language
 eng
 Summary
 This brief presents a solution to the interpolation problem for arithmetically CohenMacaulay (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 selfcontained, 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
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 Guardo, Elena
 Dewey number
 512/.44
 Index
 index present
 LC call number
 QA251.3
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Van Tuyl, Adam
 Series statement
 SpringerBriefs in mathematics
 http://library.link/vocab/subjectName

 Mathematics
 Geometry, Algebraic
 Commutative algebra
 Commutative rings
 Geometry, Projective
 Label
 Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1 Introduction  2 The biprojective space P1 x P1  3 Points in P1 x P1  4 Classification of ACM sets of points in P1 x P1  5 Homological invariants  6 Fat points in P1 x P1  7 Double points and their resolution  8 Applications  References  Index
 Control code
 SPR930702794
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319241647
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1 Introduction  2 The biprojective space P1 x P1  3 Points in P1 x P1  4 Classification of ACM sets of points in P1 x P1  5 Homological invariants  6 Fat points in P1 x P1  7 Double points and their resolution  8 Applications  References  Index
 Control code
 SPR930702794
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319241647
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
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