descriptionPublicationkeyboard_double_arrow_right Article , Preprint 28 Oct 2016Embargo end date: 01 Jan 2014 English Publisher:Informa UK LimitedJournal:Experimental Mathematics, volume 27, pages 147-178 (issn: 1058-6458, eissn: 1944-950X,

Authors: Enolski, Viktor Z.; Fedorov, Yuri;

doi: 10.1080/10586458.2016.1236357 , 10.48550/arxiv.1411.6143

arXiv: 1411.6143

handle: 2117/121261

Algebraic Description of Jacobians Isogeneous to Certain Prym Varieties with Polarization (1,2)

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Abstract

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.

51 pages, 3 figures, 3 diagrams

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
National University of Kyiv Mohyla Academy
Ukraine

Keywords

algebraic curves, Geometry, algebraic integrable systems, FOS: Physical sciences, Prym varieties, Algebraic, Mathematics - Algebraic Geometry, Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics, :14 Algebraic geometry::14H Curves [Classificació AMS], :70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS], FOS: Mathematics, Algebraic Geometry (math.AG), :32 Several complex variables and analytic spaces::32G Deformations of analytic structures [Classificació AMS], Curves, Àrees temàtiques de la UPC::Matemàtiques i estadística, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 14K12, 14H40, 14H70, 70H06, :30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain [Classificació AMS], :Matemàtiques i estadística [Àrees temàtiques de la UPC], Classificació AMS::14 Algebraic geometry::14H Curves, Curves, Algebraic, Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain, Geometry, Algebraic, Geometria algebraica, Classificació AMS::32 Several complex variables and analytic spaces::32G Deformations of analytic structures, Corbes algebraiques, Exactly Solvable and Integrable Systems (nlin.SI)

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