Enriched curves and their tropical counterpart

TL;DR

This paper introduces a tropical analogue of enriched structures on curves, constructs their moduli space, and provides a toric description of enriched structures on fixed stable curves, bridging algebraic and tropical geometry.

Contribution

It defines tropical enriched structures, constructs their moduli space, and offers a toric description for fixed stable curves, extending Main extquoteright o's work.

Findings

Defined tropical enriched structures on curves

Constructed the moduli space of these structures

Provided a toric scheme description for fixed stable curves

Abstract

In her Ph.D. thesis, Main\`o introduced the notion of enriched structure on stable curves and constructed their moduli space. In this paper we give a tropical notion of enriched structure on tropical curves and construct a moduli space parametrizing these objects. Moreover, we use this construction to give a toric description of the scheme parametrizing enriched structures on a fixed stable curve.