Quartic 3-fold: Pfaffians, instantons and half-canonical curves
| dc.creator | Iliev, A. | |
| dc.creator | Markushevich, D. | |
| dc.date | 1999-10-25 | |
| dc.date | 1999-11-20 | |
| dc.date.accessioned | 2026-07-07T05:31:16Z | |
| dc.date.available | 2026-07-07T05:31:16Z | |
| dc.description | A generic quartic 3-fold X admits a 7-dimensional family of representations as the Pfaffian of an 8 by 8 skew-symmetric matrix of linear forms. This provides a 7-dimensional moduli space M of rank 2 vector bundles on X. A precise geometric description of a 14-dimensional family of half-canonical curves C of genus 15 in X such that the above vector bundles are obtained by Serre's construction from C is given. It is proved that the Abel-Jacobi map of this family factors through M, and the resulting map from M to the intermediate Jacobian is quasi-finite. In particular, every component of M has non-negative Kodaira dimension. Some other constructions of rank 2 vector bundles with small Chern classes are discussed; it is proved that the smallest possible charge of an instanton on X is 4. | |
| dc.description | 17 pages; an extended version: the case c_1=0, c_2=4 is added and a non-existence result for c_2<4 is proved | |
| dc.identifier | https://arxiv.org/abs/math/9910133 | |
| dc.identifier | http://arxiv.org/abs/math/9910133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79282 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J30; 14J60; 14J45 | |
| dc.title | Quartic 3-fold: Pfaffians, instantons and half-canonical curves | |
| dc.type | text |