Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)

Autor:	Enolski, V. Z., Fedorov, Yu. N.
Rok vydání:	2014
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematics - Algebraic Geometry 14K12 14H40 14H70 70H06
Druh dokumentu:	Working Paper
Popis:	For a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated to such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties. We also consider some special cases of the covering C -> E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of 3 different elliptic curves. Our description is accompanied with explicit numerical examples. Comment: 51 pages, 3 figures, 3 diagrams
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1411.6143 Zobrazit plný text záznamu View this record from Arxiv