Towards a tropical Hodge bundle
arXiv:1701.04385 · doi:10.1007/978-1-4939-7486-3_16
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 $Î$, the associated canonical linear system $\vert K_Î\vert$ 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