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

By Elena Guardo,Adam Van Tuyl

ISBN-10: 3319241648

ISBN-13: 9783319241647

This short provides 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 many of the present threads within the literature in this subject with the purpose of supplying a self-contained, unified advent whereas additionally advancing a few new rules.  The suitable structures regarding multiprojective areas are reviewed first, via the elemental homes 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 could be computed and, for this reason, remedy the interpolation challenge.  In next chapters, they think about fats issues and double issues in P^1 x P^1 and display how one can use their effects to respond to questions and difficulties of curiosity in commutative algebra.  Throughout the booklet, chapters finish with a quick historic review, citations of similar effects, and, the place suitable, open questions that can motivate destiny learn.  Graduate scholars and researchers operating in algebraic geometry and commutative algebra will locate this booklet to be a important 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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