The rank-one limit of the Fourier-Mukai transform

TL;DR

This paper derives a formula describing how the Fourier-Mukai transform specializes on semi-abelian varieties with torus rank 1, advancing understanding of their geometric and categorical properties.

Contribution

It provides the first explicit formula for the specialization of the Fourier-Mukai transform in the rank-one semi-abelian setting.

Findings

Explicit formula for the Fourier-Mukai transform specialization

Enhanced understanding of semi-abelian varieties

Potential applications in algebraic geometry

Abstract

We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.