The theta divisior of the bidegree (2,2) threefold in ${\bf P}^{2} \times {\bf P}^{2}$
| dc.creator | Iliev, Atanas | |
| dc.date | 1994-02-03 | |
| dc.date.accessioned | 2026-07-07T09:05:59Z | |
| dc.date.available | 2026-07-07T09:05:59Z | |
| dc.description | Let T be a general bidegree (2,2) divisor in the product of two projective planes. Recently A.Verra proved that the existence of two conic bundle structures (c.b.s.) on T implies a new counterexample to the Torelli theorem for Prym varieties. Let J(T) be the jacobian of T. In this paper we prove that any of the two c.b.s. on T admits a parametrisation of the theta divisor of J(T) by the Abel-Jacobi image of a special family of elliptic curves of degree 9 (minimal sections of the given c.b.s.) on T. This result is an analogue of the well-known Riemann theorem for curves. In particular, this implies some results about K3 surfaces and plane sextics with vanishing theta-null. Further we use once again the geometry of curves on T, in order to prove the Torelli theorem for the bidegree (2,2) threefolds. | |
| dc.description | 32 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9402001 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9402001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149863 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The theta divisior of the bidegree (2,2) threefold in ${\bf P}^{2} \times {\bf P}^{2}$ | |
| dc.type | text |