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

✍ Scribed by Masayuki Hirokado

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 186 KB
• Volume: 162
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00022-6

✦ Synopsis

Let X be a Calabi-Yau threefold deÿned over an algebraically closed ÿeld 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 ÿber products of elliptic and quasi-elliptic rational surfaces over P 1 . These Calabi-Yau threefolds turn out to be unirational, have ÿbrations which are not generically smooth. We shall also observe their Artin-Mazur formal groups and the Hodge duality.