Autoduality holds for a degenerating abelian variety

TL;DR

This paper proves that specific degenerate abelian varieties, including compactified Jacobians of nodal curves, satisfy autoduality, using a comparison theorem linking Picard schemes to Néron models.

Contribution

It establishes autoduality for degenerate abelian varieties and introduces a comparison theorem relating Picard schemes to Néron models.

Findings

Autoduality holds for certain degenerate abelian varieties.

The total space of the family of compactified Jacobians has rational singularities.

A new comparison theorem relates Picard schemes to Néron models.

Abstract

We prove that certain degenerate abelian varieties, the compactified Jacobian of a nodal curve and a stable quasiabelian variety, satisfy autoduality. We establish this result by proving a comparison theorem that relates the associated family of Picard schemes to the N\'eron model, a result of independent interest. In our proof, a key fact is that the total space of a suitable family of compactified Jacobians has rational singularities.