Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic involutions on deformations of K3^[2]   Let X be a Hyperk\"{a}hler variety deformation equivalent to the Hilbert
square on a K3 surface and let f be an involution preserving the symplectic
form. We prove that the fixed locus of f consists of 28 isolated points and 1
K3 surface, moreover the anti-invariant lattice of the induced involution on
H^2(X,Z) is isomorphic to E_8(-2). Finally we prove that any couple consisting
of one such variety and a symplectic involution on it can be deformed into a
couple consisting of the Hilbert square of a K3 surface and the involution
induced by a Nikulin involution on the K3 surface.

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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org