Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of Koszul algebras defined by four quadrics   Avramov, Conca, and Iyengar ask whether $\beta_i^S(R) \leq \binom{g}{i}$ for
all $i$ when $R=S/I$ is a Koszul algebra minimally defined by $g$ quadrics. In
recent work, we give an affirmative answer to this question when $g \leq 4$ by
completely classifying the possible Betti tables of Koszul algebras defined by
height-two ideals of four quadrics. Continuing this work, the current paper
proves a structure theorem for Koszul algebras defined by four quadrics. We
show that all these Koszul algebras are LG-quadratic, proving that an example
of Conca of a Koszul algebra that is not LG-quadratic is minimal in terms of
number of defining equations. We then characterize precisely when these rings
are absolutely Koszul, and establish the equivalence of the absolutely Koszul
and Backelin--Roos properties up to field extensions for such rings (in
characteristic zero). The combination of the above paper with the current one
provides a fairly complete picture of all Koszul algebras defined by $g \leq 4$
quadrics.

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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph