In this paper, we present a unified study of the moduli space of tropical curves and Outer space which we link via period maps to the moduli space of tropical abelian varieties and the space of positive definite quadratic forms. Our aim is to exhibit Outer space and the space of positive definite quadratic forms as analogues of Teichm¨uller space and Siegel space, respectively, in tropical geometry. All these spaces and the maps among them are described within the category of ideal stacky fans, which we describe in detail.
Chan, M., MASCARENHAS MELO, A.m., Viviani, F. (2013). Tropical Teichmuller and Siegel spaces. In Erwan Brugallé, Mariá Angélica Cueto, Alicia Dickenstein, Eva-Maria Feichtner, Ilia Itenberg (a cura di), Algebraic and Combinatorial Aspects of Tropical Geometry (pp. 45-85). American Mathematical Society [10.1090/conm/589/11742].
Tropical Teichmuller and Siegel spaces
VIVIANI, FILIPPO
2013-01-01
Abstract
In this paper, we present a unified study of the moduli space of tropical curves and Outer space which we link via period maps to the moduli space of tropical abelian varieties and the space of positive definite quadratic forms. Our aim is to exhibit Outer space and the space of positive definite quadratic forms as analogues of Teichm¨uller space and Siegel space, respectively, in tropical geometry. All these spaces and the maps among them are described within the category of ideal stacky fans, which we describe in detail.| File | Dimensione | Formato | |
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