Unirationality of Ueno-Campana's threefold (Q470885)

The paper under review proves that a threefold constructed by \textit{K. Ueno} [Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack. York: Springer-Verlag (1975; Zbl 0299.14007)] and revisited by \textit{F. Campana} [in: Classification of algebraic varieties. Based on the conference on classification of varieties, Schiermonnikoog, Netherlands, May 2009. Zürich: European Mathematical Society (EMS). 115--121 (2011; Zbl 1219.14063)] is unirational, thus answering a question of Campana and Ueno. The proof is by explicitly writing down an equation for the affine part and noticing that this is a conic bundle with a multisection which is a rational surface. Note that Colliot-Thélène has proved that the same example is rational [``Rationalité d'un fibré en coniques'', preprint, \url{arxiv 1310.5402}].