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

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 a number of the present threads within the literature in this subject with the purpose of delivering a self-contained, unified advent whereas additionally advancing a few new rules.  The correct 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, accordingly, 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 reply to questions and difficulties of curiosity in commutative algebra.  Throughout the ebook, chapters finish with a short ancient evaluation, citations of comparable effects, and, the place appropriate, open questions which can encourage destiny examine.  Graduate scholars and researchers operating in algebraic geometry and commutative algebra will locate this ebook to be a necessary contribution to the literature.

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