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The Resource Arithmetically Cohen-Macaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)

Arithmetically Cohen-Macaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)

Label
Arithmetically Cohen-Macaulay sets of points in P1 × P1
Title
Arithmetically Cohen-Macaulay sets of points in P1 × P1
Statement of responsibility
Elena Guardo, Adam Van Tuyl
Creator
Contributor
Author
Subject
Language
eng
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
Member of
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 Cohen-Macaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)
Instantiates
Publication
Copyright
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 Cohen-Macaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)
Publication
Copyright
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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