I'm at UGA for the week, in between SWAG and TAAAG. Today Danny Krashen gave a great talk on this paper of Auel, First, and Williams. The paper is one of the latest in a long tradition of papers which construct counterexamples by making a topological computation and then approximating the relevant topological spaces by algebraic varieties. (To my knowledge, this technique began with Totaro, but it has been exploited to great effect by Antieau, Williams, and most recently, fellow Ravi student Arnav Tripathy.) ...
Read MoreFamilies of Curves Wanted
An interesting problem
Let \(n\) be a large positive integer. Recently I've been looking for a family of curves \(f_n: \mathscr{C}_n\to \mathbb{P}^1\) with the following properties:
- \(f_n\) is flat and proper of relative dimension \(1\),
- the general fiber of \(f_n\) is smooth, and the family is not isotrivial
- every singularity that appears in a fiber of \(f_n\) is etale-locally of the form $$xy=t^n$$ where \(t\) is a parameter on \(\mathbb{P}^1\)...