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Degeneration of intermediate Jacobians and the Torelli theorem

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arxiv 1809.08604 v2 pith:NOWNVBKT submitted 2018-09-23 math.AG

classification math.AG
keywords intermediatecurvedegenerationjacobiansmoduliranksecondtheorem
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abstract

Mumford and Newstead generalized the classical Torelli theorem to higher rank i.e., a smooth, projective curve $X$ is uniquely determined by the second intermediate Jacobian of the moduli space of stable rank $2$ bundles on $X$, with fixed odd degree determinant. In this article we prove the analogous result in the case $X$ is an irreducible nodal curve with one node. As a byproduct, we obtain the degeneration of the second intermediate Jacobians and the associated N\'{e}ron model of a family of such moduli spaces.

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  1. Generators of the cohomology ring, after Newstead

    math.AG 2019-08 conditional novelty 6.0 of 10

    For an irreducible nodal curve with one node, the cohomology ring of the Simpson moduli space of rank 2 semistable sheaves with fixed odd determinant has a minimal set of generators obtained by degenerating Newstead's...

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