Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conic intersections, Maximal Cohen-Macaulay modules and the Four
  Subspace problem   Let $X$ be a set of $4$ generic points in $\mathbb{P}^2$ with homogeneous
coordinate ring $R$. We classify indecomposable graded MCM modules over $R$ by
reducing the classification to the Four Subspace problem solved by Nazarova and
Gel$'$fand-Ponomarev, or equivalently to the representation theory of the
$\widetilde{D}_4$ quiver. In particular, the $\mathbb{P}^1$ tubular family of
regular representations corresponds to matrix factorizations of the pencil of
conics going through $X$, with smooth conics $Q_{t}$ corresponding to rank one
tubes and the singular conics $Q_0, Q_1, Q_{\infty}$ giving the remaining rank
two tubes. As applications we determine the Ulrich modules over $R$ and we
identify the preprojective algebra of type $\widetilde{D}_4$ as the diagonal
part of the Yoneda algebra of a Koszul $R$-module.

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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: alg-geom