Zoom link:  https://princeton.zoom.us/j/91248028438

In positive characteristic, there exist fibrations between smooth varieties where every fiber is singular or even non-reduced. In the latter case, the generic fiber of the fibration is geometrically non-reduced. We study the failure of generic smoothness and obtain a structural result about geometrically non-reduced varieties, with applications to Fano varieties.

This is joint work with Joe Waldron.