Colloquium

On the Hilbert Property and the topology of algebraic varieties

Umberto Zannier, Scuola Normale - Pisa and IAS - Princeton:

Thursday, April 11th, 2019
3:30 PM - 4:30 PM
Hylan 1106A

The Hilbert Property for an algebraic variety refers to the existence of “sufficiently many” rational points on it; it is linked with Hilbert Irreducibility Theorem, and is relevant e.g. for the Inverse Galois Problem of constructing a given finite group as a Galois group over the field Q.

Fairly recently it has been noted that the property is related with the topological fundamental group of the complex points of the variety. In particular, this viewpoint leads to new examples of failure of the Hilbert Property (for certain surfaces).

In the talk we shall give an overview of this, and also how the Hilbert Property holds for some non-rational surfaces, as the Fermat quartic
defined in P_3 by x^4+y^4=z^4+w^4 (whereas previous examples involved rational varieties).

Event contact: hazel dot mcknight at rochester dot edu