Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular sheaves on hyperk\"ahler fourfolds of Kummer type   We partially extend to hyperk\"ahler fourfolds of Kummer type the results on
hyperk\"ahler varieties of type $K3^{[2]}$ proved in a previous paper. We show
that if $(M,h)$ is a general polarized HK fourfold of Kummer type such that
$q_M(h)\equiv -6\pmod{16}$ and the divisibility of $h$ is $2$, then there
exists a slope stable rank $4$ vector bundle ${\mathscr F}$ on $M$ such that $
c_1({\mathscr F})= h$ and $\Delta({\mathscr F})=c_2(M)$. Moreover if ${\mathscr
F}$ is such a vector bundle and $\varphi$ is an automorphism of $M$ acting
trivially on $H^2(M)$, then $\varphi^{*}({\mathscr F})$ is isomorphic to
${\mathscr F}$. Lastly, the general such ${\mathscr F}$ is rigid. (There is a
similar result for polarizations $h$ such that $q_M(h)\equiv -6\pmod{144}$ and
the divisibility of $h$ is $6$.) We are motivated by the desire to describe
explicitly a locally complete family of polarized HK fourfolds of Kummer type.

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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol