Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering diagrams, stability conditions, and coherent sheaves on
  $\mathbb{P}^2$   We show that a purely algebraic structure, a two-dimensional scattering
diagram, describes a large part of the wall-crossing behavior of moduli spaces
of Bridgeland semistable objects in the derived category of coherent sheaves on
$\mathbb{P}^2$. This gives a new algorithm computing the Hodge numbers of the
intersection cohomology of the classical moduli spaces of Gieseker semistable
sheaves on $\mathbb{P}^2$, or equivalently the refined Donaldson-Thomas
invariants for compactly supported sheaves on local $\mathbb{P}^2$.
  As applications, we prove that the intersection cohomology of moduli spaces
of Gieseker semistable sheaves on $\mathbb{P}^2$ is Hodge-Tate, and we give the
first non-trivial numerical checks of the general $\chi$-independence
conjecture for refined Donaldson-Thomas invariants of one-dimensional sheaves
on local $\mathbb{P}^2$.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int