Enriched curves and their tropical counterpart

Abstract

In her Ph.D. thesis, Mainò 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.

arXiv comment41 pages, 13 figures; final version, to appear in Ann. Inst. Fourier