Birational invariants(Distinguished Lecture at BICMR)
主 题: Birational invariants(Distinguished Lecture at BICMR)
报告人: Professor Jean-Louis Colliot-Thélène (CNRS/Universit'e Paris-Sud,France)
时 间: 2015-11-18 14:00 - 15:00
地 点: Room 77201, Yard 78, Beijing International Center for Mathematical Research
Given a rationally connected variety over the complex field, one may ask whether it is stably rational, i.e. whether after possibly multiplication by a projective space it becomes birational to a projective space. One classical tool used to disprove such a statement is the Artin-Mumford invariant (1972). For smooth hypersurfaces of dimension at least three, this invariant vanishes. In 2013, Claire Voisin introduced a degeneration method which also leads to disproof of stable rationality for suitable varieties. The method was generalized by Alena Pirutka and the speaker in 2014 and it has been applied by several authors to many types of rationally connected varieties, in particular to quartic hypersurfaces. B. Totaro (2015) combined the method with a technique of Koll\'ar (1995) on differentials in positive characteristic. I shall survey the method and its very concrete applications.