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

By Elena Guardo,Adam Van Tuyl

This short offers an answer to the interpolation challenge for arithmetically Cohen-Macaulay (ACM) units of issues within the multiprojective house P^1 x P^1.  It collects many of the present threads within the literature in this subject with the purpose of offering a self-contained, unified advent whereas additionally advancing a few new principles.  The proper buildings regarding multiprojective areas are reviewed first, via the fundamental houses of issues in P^1 x P^1, the bigraded Hilbert functionality, and ACM units of issues.  The authors then convey how, utilizing a combinatorial description of ACM issues in P^1 x P^1, the bigraded Hilbert functionality may be computed and, accordingly, clear up the interpolation challenge.  In next chapters, they think about fats issues and double issues in P^1 x P^1 and exhibit the way to use their effects to reply to questions and difficulties of curiosity in commutative algebra.  Throughout the booklet, chapters finish with a short ancient evaluate, 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 publication to be a necessary contribution to the literature.

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