On the geometry of Abel maps for nodal curves

TL;DR

This paper investigates the conditions under which Abel maps can be extended to nodal curves, providing local criteria and constructing Abel maps for certain reducible curves.

Contribution

It introduces local conditions for Abel map existence on nodal curves and constructs Abel maps for all degrees on two-component nodal curves.

Findings

Established local conditions for Abel map existence on nodal curves.

Constructed Abel maps for any degree on two-component nodal curves.

Extended Abel map theory to singular, reducible curves.

Abstract

In this paper we give local conditions to the existence of Abel maps for nodal curves that are limits of Abel maps for smooth curves. We use this result to construct Abel maps for any degree for nodal curves with two components.