On the tropical Torelli map
Algebraic Geometry
2010-11-24 v5 Combinatorics
Abstract
We construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties, working in the category of (what we call) stacky fans. We define the tropical Torelli map between these two moduli spaces and we study the fibers (tropical Torelli theorem) and the image of this map (tropical Schottky problem). Finally we determine the image of the planar tropical curves via the tropical Torelli map and we use it to give a positive answer to a question raised by Namikawa on the compactified classical Torelli map.
Cite
@article{arxiv.0907.3324,
title = {On the tropical Torelli map},
author = {Silvia Brannetti and Margarida Melo and Filippo Viviani},
journal= {arXiv preprint arXiv:0907.3324},
year = {2010}
}
Comments
36 pages. Final section updated. Final version, to appear in Adv. Math