Curves, surfaces and singularities in positive characteristic

Series of talks

In May 2023, I decided to give three talks in Warwick about the theory of curves, surfaces and their singularities in positive characteristic.

  • In the first talk, I motivated with some examples why we should be interested in studying geometry in positive characteristic and how it differs from characteristic zero, focusing in the case of curves.
  • In the second talk, I explained the theory of rational double points in surfaces and how these can be studied from different points of view: topological, analytical, in terms of their resolution, and as quotients of the affine plane by the action of finite groups.
  • In the third talk, I explained Artin's paper on the classification of rational double points in positive characteristic and how in this setting the quotients by finite groups can be replaced by suitable quotients by a group scheme.

These are some handwritten notes that I used as guide for the first of the talks: