Geodesic
From real affine geometry to complex geometry
Mark Gross1 ; Bernd Siebert2
1 Department of Mathematics<br/> University of California, San Diego<br/> La Jolla, CA 92093-0112
2 Department Mathematik<br/>Universität Hamburg<br/> 20146 Hamburg<br/> Germany
Annals of mathematics, Tome 174 (2011) no. 3, pp. 1301-1428.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We construct from a real affine manifold with singularities (a tropical manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking feature of our approach is that it yields an explicit and canonical order-by-order description of the degeneration via families of tropical trees.
This gives complete control of the $B$-model side of mirror symmetry in terms of tropical geometry. For example, we expect that our deformation parameter is a canonical coordinate, and expect period calculations to be expressible in terms of tropical curves. We anticipate this will lead to a proof of mirror symmetry via tropical methods.
DOI : 10.4007/annals.2011.174.3.1

Mark Gross 1 ; Bernd Siebert 2

1 Department of Mathematics<br/> University of California, San Diego<br/> La Jolla, CA 92093-0112
2 Department Mathematik<br/>Universität Hamburg<br/> 20146 Hamburg<br/> Germany 
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Mark Gross; Bernd Siebert. From real affine geometry to complex geometry. Annals of mathematics, Tome 174 (2011) no. 3, pp. 1301-1428. doi : 10.4007/annals.2011.174.3.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.3.1/

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