Moduli spaces of rational weighted stable curves and tropical geometry

Renzo Cavalieri; Simon Hampe; Hannah Markwig; Dhruv Ranganathan

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arXiv · 1404.7426

Moduli spaces of rational weighted stable curves and tropical geometry

Renzo Cavalieri·Simon Hampe·Hannah Markwig·Dhruv Ranganathan

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Abstract

We study moduli spaces of rational weighted stable tropical curves, and their connections with the classical Hassett spaces. Given a vector w of weights, the moduli space of tropical w-stable curves can be given the structure of a balanced fan if and only if w has only heavy and light entries. In this case, we can express the moduli space as the Bergman fan of a graphic matroid. Furthermore, we realize the tropical moduli space as a geometric tropicalization, and as a Berkovich skeleton, of the classical moduli space. This builds on previous work of Tevelev, Gibney--Maclagan, and Abramovich--Caporaso--Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fiber products of unweighted spaces, and explore parallels with the algebraic world.

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Renzo Cavalieri, Simon Hampe, Hannah Markwig, Dhruv Ranganathan. 2014-04-29. Moduli spaces of rational weighted stable curves and tropical geometry. https://arxiv.org/abs/1404.7426

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