English

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.

Keywords

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

R2 v1 2026-06-21T18:49:57.132Z