Download PDF by Elena Guardo,Adam Van Tuyl: Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1

By Elena Guardo,Adam Van Tuyl

ISBN-10: 3319241648

ISBN-13: 9783319241647

This short offers an answer to the interpolation challenge for arithmetically Cohen-Macaulay (ACM) units of issues within the multiprojective area P^1 x P^1.  It collects some of the present threads within the literature in this subject with the purpose of delivering a self-contained, unified creation whereas additionally advancing a few new rules.  The correct buildings relating to multiprojective areas are reviewed first, through the elemental houses of issues in P^1 x P^1, the bigraded Hilbert functionality, and ACM units of issues.  The authors then express how, utilizing a combinatorial description of ACM issues in P^1 x P^1, the bigraded Hilbert functionality might be computed and, therefore, resolve the interpolation challenge.  In next chapters, they think about fats issues and double issues in P^1 x P^1 and show the way to use their effects to respond to questions and difficulties of curiosity in commutative algebra.  Throughout the booklet, chapters finish with a quick historic assessment, citations of similar effects, and, the place appropriate, open questions that can encourage destiny examine.  Graduate scholars and researchers operating in algebraic geometry and commutative algebra will locate this publication to be a invaluable contribution to the literature.

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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 (SpringerBriefs in Mathematics) by Elena Guardo,Adam Van Tuyl

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