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SpringerBriefs in Mathematics

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

Authors: Guardo, Elena, Van Tuyl, Adam

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  • Authors are the leading experts on the subject of arithmetically Cohen-Macaulay sets of points in multiprojective spaces
  • All necessary prerequisites are clearly explained and illustrated with carefully chosen examples
  • Presents a solution to the interpolation problem for ACM sets of points in P^1 x P^1 along with several applications
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eBook 41,64 €
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  • ISBN 978-3-319-24166-1
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Softcover 51,99 €
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  • ISBN 978-3-319-24164-7
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  • Usually dispatched within 3 to 5 business days.
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About this book

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.

About the authors

Elena Guardo, PhD, is an Associate Professor in the Department of Mathematics and Computer Sciences at the University of Catania in Italy.
Adam Van Tuyl, PhD, is an Associate Professor in the Department of Mathematics and Statistics at McMaster University in Hamilton, Ontario, Canada.

Reviews

“The present monograph is nicely written, contains some interesting examples, and almost self-contained. It provides a nice introduction to the interpolation problem for products of projective spaces. In my view, this monograph is adequate for advanced undergraduate students. … I can fully recommend this monograph.” (Piotr Pokora, zbMATH 1346.13001, 2016)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-24166-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-24164-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
The Authors
eBook ISBN
978-3-319-24166-1
DOI
10.1007/978-3-319-24166-1
Softcover ISBN
978-3-319-24164-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
VIII, 134
Number of Illustrations
25 illustrations in colour
Topics