Autoduality of the compactified Jacobian
| dc.creator | Esteves, Eduardo | |
| dc.creator | Gagne, Mathieu | |
| dc.creator | Kleiman, Steven | |
| dc.date | 1999-11-10 | |
| dc.date.accessioned | 2026-07-07T05:31:32Z | |
| dc.date.available | 2026-07-07T05:31:32Z | |
| dc.description | We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map A_L: C->J, which maps C into its compactified Jacobian, and form its pullback map A_L^*: Pic^0_J to J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, points of multiplicity 2, then A_L^* is an isomorphism, and forming it commutes with specializing C. Much of our work is valid, more generally, for a family of curves with, at worst, points of embedding dimension 2. In this case, we use the determinant of cohomology to construct a right inverse to A_L^*. Then we prove a scheme-theoretic version of the theorem of the cube, generalizing Mumford's, and use it to prove that A_L^* is independent of the choice of L. Finally, we prove our autoduality theorem: we use the presentation scheme to achieve an induction on the difference between the arithmetic and geometric genera; here, we use a few special properties of points of multiplicity 2. | |
| dc.description | Plain TeX, 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/9911071 | |
| dc.identifier | http://arxiv.org/abs/math/9911071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79380 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H40 (Primary) 14K30, 14H20 (Secondary) | |
| dc.title | Autoduality of the compactified Jacobian | |
| dc.type | text |