A fundamental question about systems of polynomial equations is whether their solution set can be parametrized by rational functions i.e. is "unirational". The classical work of Lüroth and Castelnuovo give complete characterization of when unirationality occurs for the cases of dimension 1 and -- over fields of characteristic zero -- dimension 2. However, in positive characteristic, unirationality of surfaces is poorly understood. Inspired by jet bundle techniques developed for studying the hyperbolicity of algebraic varieties, I will construct obstructions to unirationality and give examples of some surfaces these methods can prove are not unirational.
The talk will take place in PB 255.