The Resource Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1, by Elena Guardo, Adam Van Tuyl, (electronic resource)

Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1, by Elena Guardo, Adam Van Tuyl, (electronic resource)

Label
Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
Title
Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
Statement of responsibility
by Elena Guardo, Adam Van Tuyl
Creator
Contributor
Author
Provider
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 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
Member of
http://library.link/vocab/creatorName
Guardo, Elena
Image bit depth
0
LC call number
QA251.3
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Van Tuyl, Adam
  • SpringerLink
Series statement
SpringerBriefs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Geometry, Algebraic
  • Commutative algebra
  • Commutative rings
  • Geometry, Projective
  • Mathematics
  • Commutative Rings and Algebras
  • Algebraic Geometry
  • Projective Geometry
Label
Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1, by Elena Guardo, Adam Van Tuyl, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
1st ed. 2015.
Extent
VIII, 134 p. 25 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319241661
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-24166-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-24166-1
Label
Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1, by Elena Guardo, Adam Van Tuyl, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
1st ed. 2015.
Extent
VIII, 134 p. 25 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319241661
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-24166-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-24166-1

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