Topology of tropical moduli spaces of weighted stable curves in higher genus

Abstract: The space of tropical weighted curves of genus g and volume 1 is the dual complex of the divisor of singular curves in Hassett’s moduli space of weighted stable genus g curves. One can derive plenty of topological properties of the Hassett spaces by studying the topology of these dual complexes. In this talk, we show that the spaces of tropical weighted curves of genus g and volume 1 are simply-connected for all genus greater than zero and all rational weights, under the framework of symmetric Delta-complexes and via a result by Allcock-Corey-Payne 19. We also calculate the Euler characteristics of these spaces and the top weight Euler characteristics of the classical Hassett spaces in terms of the combinatorics of the weights. I will also discuss some work in progress on a geometric group approach to simple connectivity of these spaces. This is joint work with Siddarth Kannan, Stefano Serpente, and Claudia Yun.

algebraic geometrycombinatorics

Audience: researchers in the topic

Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

Please send an email to one of the organizers at the latest one day before a session if you wish to receive the Zoom link and password.

Videos of some past talks are available on YouTube here, while some slides can be found here.