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 creation whereas additionally advancing a few new rules.  The proper structures with regards to multiprojective areas are reviewed first, by way of the fundamental homes 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 might be computed and, hence, resolve 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 evaluate, citations of comparable effects, and, the place appropriate, open questions which could motivate destiny examine.  Graduate scholars and researchers operating in algebraic geometry and commutative algebra will locate this publication to be a worthy 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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