Towards a tropical Hodge bundle

Abstract

The moduli space $M_g^{trop}$ of tropical curves of genus $g$ is a generalized cone complex that parametrizes metric vertex-weighted graphs of genus $g$. For each such graph $\Gamma$, the associated canonical linear system $|K_{\Gamma }|$ has the structure of a polyhedral complex. In this article we propose a tropical analogue of the Hodge bundle on $M_g^{trop}$ and study its basic combinatorial properties. Our construction is illustrated with explicit computations and examples.

19 pages, 10 figures

References in corpus (4)

• Moduli spaces of rational tropical curves
• The tropicalization of the moduli space of curves II: Topology and applications
• Topology of the tropical moduli spaces $M_{2,n}$
• Computing Linear Systems on Metric Graphs

Cited by in corpus (3)

• Compactification of strata of abelian differentials
• Realizability of tropical canonical divisors
• Realizability of tropical pluri-canonical divisors