Products of Jacobians as Prym-Tyurin varieties
A. Carocca, H. Lange, R. E. Rodriguez, A. M. Rojas

TL;DR
This paper demonstrates that the product of Jacobian varieties of certain algebraic curves can be endowed with a Prym-Tyurin structure of explicitly computable smaller exponent, providing new insights into their geometric and algebraic properties.
Contribution
It constructs explicit Prym-Tyurin structures of smaller exponent on products of Jacobians of curves, improving known bounds and offering explicit correspondences.
Findings
Product of Jacobians admits Prym-Tyurin structure of exponent n^{m-1}
Exponent is smaller than previously known for arbitrary abelian varieties
Explicit correspondences are provided for the Prym-Tyurin structures
Abstract
Let denote smooth projective curves of genus over an algebraically closed field of characteristic 0 and let denote any integer at least equal to . We show that the product of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent . This exponent is considerably smaller than the exponent of the structure of a Prym-Tyurin variety known to exist for an arbitrary principally polarized abelian variety. Moreover it is given by explicit correspondences.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Advanced Algebra and Geometry
