On the tropical Torelli map

Details On the tropical Torelli map On the tropical Torelli map

2009-07-19

arxiv.org/abs/0907.3324v5

Advances in Mathematics 226 (2011), 2546-2586

Mathematics

Algebraic Geometry

36 pages. Final section updated. Final version, to appear in Adv. Math

Scientific paper

10.1016/j.aim.2010.09.011

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.

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