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000737558 019__ $$a931592363
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000737558 1001_ $$aGuardo, Elena,$$eauthor.
000737558 24510 $$aArithmetically Cohen-Macaulay sets of points in P¹ × P¹$$h[electronic resource] /$$cElena Guardo, Adam Van Tuyl.
000737558 264_1 $$aCham :$$bSpringer,$$c[2015].
000737558 264_4 $$c©2015
000737558 300__ $$a1 online resource.
000737558 336__ $$atext$$btxt$$2rdacontent
000737558 337__ $$acomputer$$bc$$2rdamedia
000737558 338__ $$aonline resource$$bcr$$2rdacarrier
000737558 4901_ $$aSpringerBriefs in mathematics
000737558 504__ $$aIncludes bibliographical references and index.
000737558 5050_ $$a1 Introduction -- 2 The biprojective space P¹ x P¹ -- 3 Points in P¹ x P¹ -- 4 Classification of ACM sets of points in P¹ x P¹ -- 5 Homological invariants -- 6 Fat points in P¹ x P¹ -- 7 Double points and their resolution -- 8 Applications -- References -- Index.
000737558 506__ $$aAccess limited to authorized users.
000737558 520__ $$aThis brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P̂1 x P̂1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P̂1 x P̂1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P̂1 x P̂1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem. In subsequent chapters, they consider fat points and double points in P̂1 x P̂1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra. Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research. Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature.
000737558 650_0 $$aMathematics.
000737558 650_0 $$aGeometry, Algebraic.
000737558 650_0 $$aCommutative algebra.
000737558 650_0 $$aCommutative rings.
000737558 650_0 $$aGeometry, Projective.
000737558 7001_ $$aVan Tuyl, Adam,$$eauthor.
000737558 77608 $$iPrint version:$$aGuardo, Elena$$tArithmetically Cohen-Macaulay Sets of Points in P^1 x P^1$$dCham : Springer International Publishing,c2015$$z9783319241647
000737558 830_0 $$aSpringerBriefs in mathematics.
000737558 85280 $$bebk$$hSpringerLink
000737558 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-24166-1$$zOnline Access$$91397441.1
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000737558 980__ $$aEBOOK
000737558 980__ $$aBIB
000737558 982__ $$aEbook
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