$R$-EQUIVALENCE ON DEL PEZZO SURFACES OF DEGREE $4$ AND CUBIC SURFACES
Résumé
We prove that there is a unique R-equivalence class on every del Pezzo surface of degree 4 defined over the Laurent field K=k((t)) in one variable over an algebraically closed field k of characteristic not equal to 2 or 5. We also prove that given a smooth cubic surface defined over ℂ((t)), if the induced morphism to the GIT compactification of smooth cubic surfaces lies in the stable locus (possibly after a base change), then there is a unique R-equivalence class.