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

Name: Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
Brand: Springer International Publishing AG
SKU: 9783319241647
Price: 276.12 RON
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Autor: Elena Guardo, Adam van Tuyl

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Editura: Springer International Publishing AG

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This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM)...

Informații despre carte

Autor

Elena Guardo, Adam van Tuyl

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2015

Pagini

134

EAN

9783319241647

ISBN

3319241648

Enbook ID

09503642

Editura

Springer International Publishing AG

Greutate

242

Dimensiuni

237 x 160 x 9

Descriere completă

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 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.

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

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