For an irreducible nodal curve of genus at least two, the cohomology ring of the moduli space of rank-two semistable sheaves with fixed odd determinant obeys the Mumford relations restricted to monodromy-invariant classes, and its Hodge-Poincare polynomial is computed explicitly.
Generators of the cohomology ring, after Newstead
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abstract
Newstead gave the generators of the cohomology ring of the moduli space of rank 2 semi-stable, torsion-free sheaves with fixed odd degree determinant over a smooth, projective curve. In this article, we generalize this result to the case when the underlying curve is irreducible, nodal. We show that these generators (of the cohomology ring in the nodal curve case) arise naturally as degeneration of Newstead's generators in the smooth curve case.
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Generalization of a conjecture of Mumford
For an irreducible nodal curve of genus at least two, the cohomology ring of the moduli space of rank-two semistable sheaves with fixed odd determinant obeys the Mumford relations restricted to monodromy-invariant classes, and its Hodge-Poincare polynomial is computed explicitly.