Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On deformations of pairs (manifold, coherent sheaf)   We analyse infinitesimal deformations of pairs $(X,\mathcal{F})$ with
$\mathcal{F}$ a coherent sheaf on a smooth projective manifold $X$ over an
algebraic closed field of characteristic $0$. We describe a differential graded
Lie algebra controlling the deformation problem, and we prove an analog of a
Mukai-Artamkin Theorem about the trace map.

25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas