Joseph Gunther : Random Hypersurfaces and Embedding Curves in Surfaces

Posted by Nathan Jones , part of the Number Theory Seminar.

At

April 20, 2016, 1 p.m.

In

SEO 1227

Abstract

We'll present two new applications of Poonen's closed-point sieve over finite fields. The first is that the obvious local obstruction to embedding a curve in a smooth surface is the only global obstruction, over any perfect field. The second is a proof of a conjecture of Vakil and Wood, on the probability that a random hypersurface slice of a smooth variety will have a given number of singularities.