Fourier transforms and Abel-Jacobi theory

TL;DR

This paper explores the connection between Fourier transforms on compactified Jacobians and logarithmic Abel-Jacobi theory, providing new formulas for pushforwards of divisor monomials related to the double ramification cycle.

Contribution

It introduces a novel relationship between Fourier transforms and Abel-Jacobi theory on moduli spaces, with explicit computations of divisor pushforwards.

Findings

Derived formulas for pushforward of divisor monomials

Connected Fourier transforms to logarithmic Abel-Jacobi theory

Provided new insights into the double ramification cycle

Abstract

We relate Fourier transforms between compactified Jacobians over the moduli space of stable curves to logarithmic Abel-Jacobi theory. As an application, we compute the pushforward of divisor monomials on compactified Jacobians in terms of the twisted double ramification cycle formula.