Potentially Stably Rational Del Pezzo Surfaces over Nonclosed Fields

Abstract

A geometrically rational surface S over a nonclosed field k is k-birational to either a del Pezzo surface of degree \(n\in [1,\ldots , 9]\) or a conic bundle (see [6]). Throughout, we assume that \(S(k)\ne \emptyset \). This implies k-rationality of S when \(n\in [5,\ldots , 9]\) or when the number of degenerate fibers of the conic bundle is at most 3.