MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY
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Publication:5739911
DOI10.1017/FMS.2016.7zbMATH Open1373.14063arXiv1404.7426OpenAlexW2963339332MaRDI QIDQ5739911
Author name not available (Why is that?)
Publication date: 6 July 2016
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1404.7426
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