An Explicit Non-smoothable Component of the Compactified Jacobian

Details An Explicit Non-smoothable Component of the Compactified Jacobian An Explicit Non-smoothable Component of the Compactified Jacobian

2011-08-12

arxiv.org/abs/1108.2706v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

This paper studies the components of the moduli space of rank 1, torsion-free sheaves, or compactified Jacobian, of a non-Gorenstein curve. We exhibit a generically reduced component of dimension equal to the arithmetic genus and prove that this is the only non-smoothable component when the curve has a unique singularity that is of finite representation type. Analogous results are proven for the Hilbert scheme of points and the Quot scheme parameterizing quotients of the dualizing sheaf.

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