Degenerations of rationally connected varieties and PAC fields

Abstract

A perfect PAC field containing an algebraically closed field is known to be $C_1$, i.e., every degeneration of a Fano complete intersection has a point. We prove that also every degeneration of a separably rationally connected variety has a point.

5 pages

References in corpus (2)

• Varieties over a finite field with trivial Chow group of 0-cycles have a rational point
• A conjecture of Ax and degenerations of Fano varieties