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Tropical modifications against superabundant curves October 02, 2009
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Mr. Erwan Brugalle
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I guess (almost?) everybody agree that it is an important issue to determine which tropical varieties and sub-varieties are the
"tropicalisation" of classical varieties and sub-varieties. In the case of tropical curves in tropical varieties, Mikhalkin gave a
sufficient condition ensuring the approximation by classical varieties. However, many tropical curves, called superabundant curves, have a space of deformation of too big dimension, and are likely not approximable. In this talk, I will explain how to use tropical modifications to deal with superabundant tropical curves in tropical varieties. In particular, I will explain how to extend Speyer's criterion for curves of genus 1 to curves of any genus. If times permits, I will also link this work with tropical tangencies.
This is a joint work with Grigory Mikhalkin.

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