Algebraic Geometry Seminar: Daniel Erman

For a smooth projective variety over a finite field, Poonen’s Bertini Theorem computes the probability that a high degree hypersurface section of that variety will be smooth.  We prove a semiample generalization of Poonen's result, where the probability of smoothness is computed as a product of local probabilities taken over the fibers of a corresponding morphism.  This is joint with Melanie Matchett Wood.