An explicit non-smoothable component of the compactified Jacobian

作者：Kass Jesse Leo^*

来源：Journal of Algebra, 2012, 370: 326-343.

DOI：10.1016/j.jalgebra.2012.07.033

• Compactified Jacobian
• Hilbert scheme
• Rank 1
• Torsion-free sheaf

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 it 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.

• 出版日期2012-11-15