Heisenberg invariant quartics and SU_C(2) for a curve of genus four
| dc.creator | Oxbury, William | |
| dc.creator | Pauly, Christian | |
| dc.date | 1997-03-21 | |
| dc.date.accessioned | 2026-07-07T09:07:13Z | |
| dc.date.available | 2026-07-07T09:07:13Z | |
| dc.description | If C is a curve of genus 4 without vanishing theta-nulls then there exists a unique (irreducible) Heisenberg-invariant quartic Q_C in |2Θ| = P^{15} such that Sing Q_C contains the image of SU_C(2), the moduli space of rank 2 vector bundles with trivial determinant. Moreover, in each eigen-P^7 of the Heisenberg action on |2Θ|, Q_C restricts to the classical Coble quartic of the corresponding Prym-Kummer variety. We compare Q_C with the hypersurface G_3 in |2Θ| of divisors containing a translate of C in J(C), and show that in the eigen-P^7s G_3 recovers Beauville--Debarre's quadrisecant planes of the Prym-Kummers (this works for any genus). Using the Recillas construction this enables us to deduce, contrary to the analogous result for genus 3, that Q_C and G_3 are distinct. | |
| dc.description | LaTeX, 36 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9703026 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9703026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150293 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Heisenberg invariant quartics and SU_C(2) for a curve of genus four | |
| dc.type | text |