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Two-coverings of Jacobians of curves of genus 2
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Flynn, E. V., Testa, Damiano and van Luijk, R.. (2012) Two-coverings of Jacobians of curves of genus 2. Proceedings of the London Mathematical Society, Vol.104 (No.2). pp. 387-429. ISSN 0024-6115
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Official URL: http://dx.doi.org/10.1112/plms/pdr012
Abstract
Given a curve C of genus 2 defined over a field k of characteristic different from 2, with a Jacobian variety J, we show that the two-coverings corresponding to elements of a large subgroup of H1(Gal(ks/k), J[2](ks)) (containing the Selmer group when k is a global field) can be embedded as an intersection of 72 quadrics in ℙ15k, just as the Jacobian J itself. Moreover, we actually give explicit equations for the models of these twists in the generic case, extending the work of Gordon and Grant which applied only to the case when all Weierstrass points are rational. In addition, we describe elegant equations of the Jacobian itself, and answer a question of Cassels and Flynn concerning a map from the Kummer surface in ℙ3 to the desingularized Kummer surface in ℙ5.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Proceedings of the London Mathematical Society |
| Publisher: | Cambridge University Press |
| ISSN: | 0024-6115 |
| Date: | February 2012 |
| Volume: | Vol.104 |
| Number: | No.2 |
| Page Range: | pp. 387-429 |
| Identification Number: | 10.1112/plms/pdr012 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/44140 |
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