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)
Resource Information
The item Arithmetically Cohen-Macaulay 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 Cohen-Macaulay 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 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
- 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 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
- 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
- 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)
- 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)
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Arithmetically-Cohen-Macaulay-sets-of-points-in/aEDmZzqAsjc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Arithmetically-Cohen-Macaulay-sets-of-points-in/aEDmZzqAsjc/">Arithmetically Cohen-Macaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
