Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Stillman bounds for all degrees   In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the
existence of a uniform upper bound for the projective dimension of all
homogeneous ideals, in polynomial rings over a field, generated by n forms of
degree at most d. Explicit values of the bounds for forms of degrees 5 and
higher are not yet known. The main result of this article is the construction
of explicit such bounds, for all degrees d, which behave like power towers of
height d^3/6+11d/6-4. This is done by establishing a bound D(k,d), which
controls the number of generators of a minimal prime over an ideal of a regular
sequence of k or fewer forms of degree d, and supplementing it into Ananyan and
Hochster's proof in order to obtain a recurrence relation.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: cond-mat