Arithmetically Cohen Macaulay Sets of Points in P 1 x P 1 is popular PDF and ePub book, written by Elena Guardo in 2015-11-25, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Arithmetically Cohen Macaulay Sets of Points in P 1 x P 1 can be Read Online from any device for your convenience.
Arithmetically Cohen Macaulay Sets of Points in P 1 x P 1 Book PDF Summary
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.
Detail Book of Arithmetically Cohen Macaulay Sets of Points in P 1 x P 1 PDF
- Author : Elena Guardo
- Release : 25 November 2015
- Publisher : Birkhäuser
- ISBN : 9783319241661
- Genre : Mathematics
- Total Page : 136 pages
- Language : English
- PDF File Size : 14,9 Mb
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