The combinatorics of the tropical Hodge bundles


Bo Lin,(UT Austin)

2018.06.25, 15:30-17:00, N109

【Abstract】The moduli space $M_g^{trop}$ of tropical curves of genus $g$ is a generalized cone complex that parameterizes metric graphs of genus $g$. For each such graph $\Gamma$, the associated canonical linear system $\vert K_\Gamma\vert$ has the structure of a polyhedral cell complex. We propose a tropical analogue of the Hodge bundle on $M_g^{trop}$ and study its combinatorial properties. Our construction is illustrated with explicit computations and examples. This is a joint work with Martin Ulirsch.