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[null,"1.","Record Nr.",null,"UNINA9910300259903321"]
[null,null,"Autore",null,"Guardo Elena"]
[null,null,"Titolo",null,"Arithmetically Cohen-Macaulay sets of points in P^1 x P^1 / / by Elena Guardo, Adam Van Tuyl"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015"]
[null,null,"ISBN",null,"3-319-24166-4"]
[null,null,"Edizione",null,"[1st ed. 2015.]"]
[null,null,"Descrizione fisica",null,"1 online resource (136 p.)"]
[null,null,"Collana",null,"SpringerBriefs in Mathematics, , 2191-8198"]
[null,null,"Disciplina",null,"516.35"]
[null,null,"Soggetti",null,"Commutative algebra"]
[{"$nulls":4},"Commutative rings"]
[{"$nulls":4},"Geometry, Algebraic"]
[{"$nulls":4},"Geometry, Projective"]
[{"$nulls":4},"Commutative Rings and Algebras"]
[{"$nulls":4},"Algebraic Geometry"]
[{"$nulls":4},"Projective Geometry"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"Sommario/riassunto","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, "]
[{"$nulls":4},"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."]