Abel maps for curves of compact type

TL;DR

This paper constructs and compares two Abel maps for stable curves of compact type, providing insights into their fibers and characterizing hyperelliptic curves with two components.

Contribution

It introduces two new Abel maps for stable curves of compact type and analyzes their fibers, offering a characterization of hyperelliptic curves with two components.

Findings

Two distinct d-th Abel maps are constructed for stable curves of compact type.

Comparison of fibers reveals structural differences between the two Abel maps.

Characterization of hyperelliptic stable curves with two components via the 2-nd Abel map.

Abstract

Recently, the first Abel map for a stable curve of genus g>1 has been constructed. Fix an integer d>0 and let C be a stable curve of compact type of genus g>1. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-nd Abel map.