A Characterization of Jacobians by the Existence of Picard Bundles
Ana Cristina L\'opez Mart\'in, Ernesto Carlo Mistretta, Dar\'io, S\'anchez G\'omez
TL;DR
This paper provides a criterion to identify Jacobian varieties among principal polarized abelian varieties based on the existence of Picard bundles, extending the understanding of their geometric structure.
Contribution
It introduces a new characterization of Jacobians using Picard bundles, building on the Matsusaka-Ran criterion.
Findings
Characterization of Jacobians via Picard bundles
Extension of Matsusaka-Ran criterion
New geometric insights into abelian varieties
Abstract
Based on the Matsusaka-Ran criterion we give a criterion to characterize when a principal polarized abelian variety is a Jacobian by the existence of Picard bundles.
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 · Nonlinear Waves and Solitons