Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal Betti Numbers and Applications to Monomial Ideals   In this short note we introduce a notion of extremality for Betti numbers of
a minimal free resolution, which can be seen as a refinement of the notion of
Mumford-Castelnuovo regularity. We show that extremal Betti numbers of an
arbitrary submodule of a free S-module are preserved when taking the generic
initial module. We relate extremal multigraded Betti numbers in the minimal
resolution of a square free monomial ideal with those of the monomial ideal
corresponding to the Alexander dual simplicial complex and generalize theorems
of Eagon-Reiner and Terai. As an application we give easy (alternative) proofs
of classical criteria due to Hochster, Reisner, and Stanley.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th