Room P3.10, Mathematics Building

Thomas Baier, Instituto Superior Técnico, Lisboa
(Tropical) Amoebas in Moment Polytopes

Considering toric deformations of complex structures, described by the symplectic potentials of Abreu and Guillemin, we study degenerate limits of holomorphic polarizations corresponding to the toric Lagrangian fibration. We use these toric metric degenerations to study the (Gromov-Hausdorff) limit of hypersurfaces and show that in Legendre transformed variables they are described by compact pieces of tropical amoebas in the sense of Gelfand-Kapranov-Zelevinsky and Mikhalkin. This talk will be based on the preprint arXiv:0806.0606 (joint work with C. Florentino, J. M. Mourão and J. P. Nunes).