A universal tropical Jacobian over $M_g^{\trop}$

Abstract

We introduce and study polystable divisors on a tropical curve, which are the tropical analogue of polystable torsion-free rank-1 sheaves on a nodal curve. We construct a universal tropical Jacobian over the moduli space of tropical curves of genus $g$. This space parametrizes equivalence classes of tropical curves of genus $g$ together with a $\mu$-polystable divisor, and can be seen as a tropical counterpart of Caporaso universal Picard scheme. We describe polyhedral decompositions of the Jacobian of a tropical curve via polystable divisors, relating them with other known polyhedral decompositions.

arXiv comment5 figures, 31 pages. New version: corrected some citations

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Cited by in corpus (1)

• Kirchhoff's theorem for Prym varieties