Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-Mukai and autoduality for compactified Jacobians II   To every reduced (projective) curve X with planar singularities one can
associate many fine compactified Jacobians, depending on the choice of a
polarization on X, which are birational (possibly non-isomorphic) Calabi-Yau
projective varieties with locally complete intersection singularities. We
define a Poincare' sheaf on the product of any two (possibly equal) fine
compactified Jacobians of X and show that the integral transform with kernel
the Poincare' sheaf is an equivalence of their derived categories. In
particular, any two fine compactified Jacobians are derived equivalent. When
applied to the same fine compactified Jacobian, one gets a Fourier-Mukai
autoequivalence, which generalizes the classical result of Mukai for Jacobians
of smooth curves (or more generally abelian varieties) and of Arinkin for
compactified Jacobians of integral curves, thus providing further evidence for
the classical limit of the geometric Langlands conjecture (as formulated by R.
Donagi and T. Pantev). As a corollary of our main result, we prove an
autoduality result for fine compactified Jacobians: there is a natural
equivariant open embedding of the connected component of the scheme
parametrizing rank-1 torsion-free sheaves on X into the connected component of
the algebraic space parametrizing rank-1 torsion-free sheaves on a given fine
compactified Jacobian of X.

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The categories of this paper are: mtrl-th
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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: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int