Seminar

A small deformation of a tropical variety corresponds in algebraic geometry to a rigid-analytic deformation of an algebraic variety. For example, a deformation of the tropicalization of the polynomial x+y-1 over a non-Archimedean field K would correspond to a polynomial ax + by + c, where |a-1|, |b-1|, and |c-1| are small; these not algebraic conditions on a,b, and c, but are open conditions in the rigid-analytic sense. I will give a brief introduction to the theory of rigid geometry, which closely paralells the theory of finite-type schemes over a non-Archimedean field, and then I will give an indication of how such methods can be used to prove a deformation-invariance result for tropical intersection numbers using a corresponding result in rigid geometry.