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The Resource Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl
Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl
Resource Information
The item Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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
 9783319241661
 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
 MATHEMATICS
 Commutative algebra
 Commutative rings
 Geometry, Algebraic
 Geometry, Projective
 Mathematics
 Algebraic geometry
 Geometry
 Algebra
 Label
 Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl
 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
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319241661
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 SpringerLink
 Other control number
 10.1007/9783319241661
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)930702794
 (OCoLC)ocn930702794
 Label
 Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl
 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
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319241661
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 SpringerLink
 Other control number
 10.1007/9783319241661
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)930702794
 (OCoLC)ocn930702794
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



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Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

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Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/ArithmeticallyCohenMacaulaysetsofpointsin/5Vediqnps3I/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/ArithmeticallyCohenMacaulaysetsofpointsin/5Vediqnps3I/">Arithmetically CohenMacaulay sets of points in P1 × P1, Elena Guardo, Adam Van Tuyl</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>