Complex surfaces 2: Minimal surfaces
Channel: Richard E Borcherds
Date: 2020-11-05

This talk is part of a series about complex surfaces, and explains what minimal surfaces are.

A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We discuss Zariski's theorem expressing a birational map in terms of blowups and blowdowns, and state Castelnuovo's criterion for a curve to be exceptional (meaning it is the inverse image of the blowup of a point). Finally we give the birational map from P2 to P1 x P1 as an example.