Remark on a theorem of Oguiso

Abstract

For a Calabi–Yau variety X, Oguiso (Math Res Lett 25(1):181–198, 2018) gave a useful criterion for primitivity of a self-map of X in terms of the associated linear map on the Néron–Severi space of X. In this short note, we prove a variant of Oguiso’s criterion and use it to verify primitivity of a certain birational automorphism of a Calabi–Yau threefold, to which Oguiso’s original criterion does not apply.