Towards a tropical hodge bundle

Abstract

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