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Title:	Algebraic description of jacobians isogeneous to certain prym varieties with polarization (1,2)
Author:	Enolski, Viktor Z.; Fedorov, Yuri
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
Abstract:	For a class of non-hyperelliptic genus 3 curves C which are twofold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated with 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 three different elliptic curves. Our description is accompanied with explicit algorithms of calculation of periods of the Prym varieties and of absolute invariants of genus 2 curves. They are followed by numerical examples, which experimentally confirm main results of the articl
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Geometry, Algebraic -Curves, Algebraic -algebraic curves -Prym varieties -algebraic integrable systems -Geometria algebraica -Corbes algebraiques -Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics -Classificació AMS::14 Algebraic geometry::14H Curves -Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain -Classificació AMS::32 Several complex variables and analytic spaces::32G Deformations of analytic structures
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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