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024 7 $a10.1007/978-3-319-24166-1
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100   $a20151125d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aArithmetically Cohen-Macaulay sets of points in P^1 x P^1 /$fby Elena Guardo, Adam Van Tuyl
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (136 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
300   $aDescription based upon print version of record.
311   $a3-319-24164-8 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- 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.
330   $aThis brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1.  It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas.  The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points.  The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem.  In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra.  Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research.  Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgebraic geometry
606   $aProjective geometry
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
606   $aProjective Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21050
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgebraic geometry.
615  0$aProjective geometry.
615 14$aCommutative Rings and Algebras.
615 24$aAlgebraic Geometry.
615 24$aProjective Geometry.
676   $a516.35
700   $aGuardo$b Elena$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755672
702   $aVan Tuyl$b Adam$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300259903321
996   $aArithmetically Cohen-Macaulay Sets of Points in P^1 x P^1$92525166
997   $aUNINA