Monday 30th of September 2024, 13:30-14:30 in HG02.052
Finn Bartsch
Nowhere reduced degenerations of varieties
When varieties (or manifolds) come in a family, there are often finitely many members of that family that are qualitatively worse behaved than the "typical" member: They have self-intersections or other features that prevent them from being a manifold. We call these objects "singular fibers". In this talk, I will focus on a particularly nasty type of singular fibers, which are the "nowhere reduced fibers". After explaining what they are and giving some examples, I will explain how the occurence of nowhere reduced fibers in a fibration impacts the geometry of the total space. If time permits, I will also briefly talk about upcoming work in which we study a specific such family with a view towards number theory.