The resolution of the universal Abel map via tropical geometry and applications
Alex Abreu, Marco Pacini

TL;DR
This paper provides an explicit resolution of the universal Abel map using tropical geometry techniques and applies this to describe the double ramification cycle in algebraic geometry.
Contribution
It introduces a new explicit resolution of the universal Abel map via tropical geometry and relates it to the double ramification cycle.
Findings
Explicit resolution of the universal Abel map constructed.
Resolution inspired by tropical analogue in generalized cone complexes.
Application to describing the double ramification cycle.
Abstract
Let and be nonnegative integers and a sequence of integers summing up to . Let be the moduli space of -pointed stable curves of genus and be the Esteves' universal Jacobian, where is a universal genus- polarization of degree . We give an explicit resolution of the universal Abel map , taking a pointed curve to . The blowup of giving rise to the resolution is inspired by the resolution of the tropical analogue of the map (in the category of generalized cone complexes). As an application, we…
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