|Location:||MSRI: Simons Auditorium|
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.