Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Syzygies of the Veronese modules   We study the minimal free resolution of the Veronese modules of the
polynomial ring in n variables, by giving a formula for the Betti numbers in
terms of the reduced homology of some skeleton of a simplicial complex. We
characterize when they are Cohen-Macaulay and we give a sufficient condition
for the linearity of their minimal free resolution. We also conjecture that in
2 variables the Veronese modules have always pure resolutions. In addition, we
give a closed formula for their Hilbert series. As an application of our
results, we calculate the complete Betti diagrams of the Veronese subrings in
three variables with degree 4 and 5, and in four variables with degree 3.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: eess