Calabi-Yau threefolds obtained as fiber products of elliptic and quasi-elliptic rational surfaces

摘要

Let X be a Calabi-Yau threefold defined over an algebraically closed field k of characteristic p > 0. It is natural to expect that X has some properties which cannot be seen in characteristic zero. To observe such phenomena, we study Calabi-Yau threefolds constructed from fiber products of elliptic and quasi-elliptic rational surfaces over P-1. These Calabi-Yau threefolds turn out to be unirational, have fibrations which are not generically smooth. We shall also observe their Artin-Mazur formal groups and the Hodge duality. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 12]