Cubic equations for the hyperelliptic locus
| dc.creator | Grushevsky, Samuel | |
| dc.date | 2005-03-02 | |
| dc.date.accessioned | 2026-07-07T05:17:36Z | |
| dc.date.available | 2026-07-07T05:17:36Z | |
| dc.description | We discuss the conjecture of Buchstaber and Krichever that their multi-dimensional vector addition formula for Baker-Akhiezer functions characterizes Jacobians among principally polarized abelian varieties, and prove that it is indeed a weak characterization, i.e. that it is true up to additional components, or true precisely under a general position assumption. We also show that this addition formula is equivalent to Gunning's multisecant formula for the Kummer variety. We then use Buchstaber-Krichever's computation of the coefficients in the addition formula to obtain cubic relations among theta functions, which (weakly) characterize the locus of hyperelliptic Jacobians among irreducible abelian varieties. In genus 3 our equations are equivalent to the vanishing of one theta-null, and thus are known classically by work of Mumford and Poor, but already for genus 4 they appear to be new. | |
| dc.identifier | https://arxiv.org/abs/math/0503026 | |
| dc.identifier | http://arxiv.org/abs/math/0503026 | |
| dc.identifier | Asian J Math, vol 8 (2004) no. 1, special issue dedicated to Yum-Tong Siu on his 60th birthday | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74361 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Cubic equations for the hyperelliptic locus | |
| dc.type | text |