Mathematics – Algebraic Geometry
Scientific paper
2009-07-19
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.
Brannetti Silvia
Melo Margarida
Viviani Filippo
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