03986nam 22007095 450 991030025990332120251116144803.03-319-24166-410.1007/978-3-319-24166-1(CKB)3710000000521712(EBL)4178724(SSID)ssj0001584858(PQKBManifestationID)16265109(PQKBTitleCode)TC0001584858(PQKBWorkID)14865075(PQKB)10141726(DE-He213)978-3-319-24166-1(MiAaPQ)EBC4178724(PPN)258862599(PPN)19052345X(EXLCZ)99371000000052171220151125d2015 u| 0engur|n|---|||||txtccrArithmetically Cohen-Macaulay sets of points in P^1 x P^1 /by Elena Guardo, Adam Van Tuyl1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (136 p.)SpringerBriefs in Mathematics,2191-8198Description based upon print version of record.3-319-24164-8 Includes bibliographical references and index.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.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.SpringerBriefs in Mathematics,2191-8198Commutative algebraCommutative ringsGeometry, AlgebraicGeometry, ProjectiveCommutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Projective Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21050Commutative algebra.Commutative rings.Geometry, Algebraic.Geometry, Projective.Commutative Rings and Algebras.Algebraic Geometry.Projective Geometry.516.35Guardo Elenaauthttp://id.loc.gov/vocabulary/relators/aut755672Van Tuyl Adamauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300259903321Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^12525166UNINA