Homogeneous Fibrations over Curves

Abstract

By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface, a projective homogeneous space admits a rational point if the elementary obstruction vanishes.

32 pages. Final version

References in corpus (1)

• Revêtements étales et groupe fondamental (SGA 1)

Cited by in corpus (2)

• Quartic del Pezzo surfaces over function fields of curves
• Integral Hodge classes on fourfolds fiberd by quadric bundles