An Explicit Non-smoothable Component of the Compactified Jacobian
Algebraic Geometry
2012-08-21 v2
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.
Cite
@article{arxiv.1108.2706,
title = {An Explicit Non-smoothable Component of the Compactified Jacobian},
author = {Jesse Leo Kass},
journal= {arXiv preprint arXiv:1108.2706},
year = {2012}
}
Comments
23 pages; expository changes, error in table corrected, notation for singularities changed; to appear in Journal of Algebra