Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact tori associated to hyperkaehler manifolds of Kummer type   Let X be a hyperkaehler manifold of Kummer type. We study the 4 dimensional
intermediate Jacobian J^3(X) constructed out of the 3rd cohomology of X,
motivated by the desire to understand the Kuga-Satake torus associated to X. We
prove that there is an embedding of Hodge structures of H^2(X) into
H^2(J^3(X)). It follows that if X is projective with polarization L, the
projective Kuga-Satake torus of (X,L) is isogenous to the fourth power of
J^3(X). By studying the cohomology ring of X, we find that there is a natural
smooth quadric Q(X) in the projectivization of H^3(X), with a natural choice of
one of the two irreducible components of the variety parametrizing maximal
linear subspaces of Q(X). Let Q^{+}(X) be the chosen irreducible component;
then it is a smooth quadric in the projectivization of S^{+}(X), one of the two
spinor representations of Spin H^3(X), where H^3(X) is equipped with the
quadratic form whose zero locus is Q(X). Gauss-Manin parallel transport
identifies the set of projectivizations of H^{2,1}(Y), for Y a deformation of
X, with an open subset of a linear section of Q^{+}(X). This amounts to an
effective description of the intermediate Jacobian J^3(X) in terms of the H.S.
on H^2(X). A simple consequence is a new proof of a result of Mongardi giving
(necessary) conditions for the action of monodromy on H^2(X). Lastly, we show
that if X is projective, then J^3(X) is an abelian fourfold of Weil type.

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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas