On the Hilbert Property and the fundamental group of algebraic varieties

Joint IAS/Princeton University Number Theory Seminar
Topic:On the Hilbert Property and the fundamental group of algebraic varieties
Speaker:Umberto Zannier
Affiliation:Scuola Normale Superiore di Pisa
Date:Tuesday, May 10
Time/Room:4:30pm - 5:30pm/Fine 214, Princeton University

This concerns recent work with P. Corvaja in which we relate the Hilbert Property for an algebraic variety (a kind of axiom linked with Hilbert Irreducibility, relevant e.g. for the Inverse Galois Problem) with the fundamental group of the variety. In particular, this leads to new examples (of surfaces) of failure of the Hilbert Property. We also prove the Hilbert Property for a non-rational surface (whereas all previous examples involved rational varieties).