Filippo Viviani
Published 2012-04-17, updated 2013-04-25Version 2
In this paper, we compare the compactified Torelli morphism (as defined by V. Alexeev) and the tropical Torelli map (as defined by the author in a joint work with S. Brannetti and M. Melo, and furthered studied by M. Chan). Our aim is twofold: on one hand, we will review the construction and main properties of the above mentioned two Torelli maps, focusing in particular on the description of their fibers achieved by the author in joint works with L. Caporaso; on the other hand, we will clarify the relationship between the two Torelli maps via the introduction of the reduction maps and the tropicalization maps.
Comments: 28 pages, final version, to appear in CRM Proceedings of the Conference Tropical and Non Archimedean Geometry (Bellairs Research Institute, May 2011)
Journal: Tropical and Non-Archimedean Geometry, Contemp. Math. 605 (2013), 181--210
On the tropical Torelli map
Compactifying the relative Picard functor over degenerations of varieties
Volumes of line bundles
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