Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monomial Resolutions   Call a monomial ideal M "generic" if no variable appears with the same
nonzero exponent in two distinct monomial generators. Using a convex polytope
first studied by Scarf, we obtain a minimal free resolution of M. Any monomial
ideal M can be made generic by deformation of its generating exponents. Thus,
the above construction yields a (usually nonminimal) resolution of M for
arbitrary monomial ideals, bounding the Betti numbers of M in terms of the
Upper Bound Theorem for Convex Polytopes.
  We show that our resolutions are DG-algebras, and consider realizability
questions and irreducible decompositions.

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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga