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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1



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Springer


Collection :

SpringerBriefs in Mathematics

Paru le : 2015-11-25



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Description
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.
Pages
134 pages
Collection
SpringerBriefs in Mathematics
Parution
2015-11-25
Marque
Springer
EAN papier
9783319241647
EAN PDF
9783319241661
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
13
Taille du fichier
3113 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
52,74 €
EAN EPUB
9783319241661
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
13
Taille du fichier
2744 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
52,74 €

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