Curves and models of curves

Speaker's Name: Tim Dokchitser
Speaker's Affiliation: Bristol
Speaker's Research Theme(s): Pure Mathematics
Abstract:
For a plane curve f(x,y)=0, a natural question is how to find a good, non-singular model and the space where it naturally lives. It is sort of classical that the answer is encoded in the Newton polygon of f, which determines a toric surface with the best geometric properties. I want to explain how this works, and how it helps to compute the genus and regular differentials of the curve directly from f. The application that inspired this was to understand regular models of curves over DVRs, and this should be useful tool in that direction. (Joint work with Gergely Jakovac.)

Venue: Physics C05