Tuesday, February 23, 2021
02/23/2021 - 9:00am
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 by showing a generalization of Tate's genus change formula, and obtain a structural result about geometrically non-reduced varieties. Our result has applications to Fano varieties. This is joint work with Joe Waldron.