An Explicit Non-smoothable Component of the Compactified Jacobian

Abstract

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.

arXiv comment23 pages; expository changes, error in table corrected, notation for singularities changed; to appear in Journal of Algebra