Time:2016-10-28, 16:00-17:30

Place:Room 1518, School of Mathematical Sciences 

Detail:  The so-called Severi inequality for complex surfaces of maximal Albanese dimension dates back to a paper of Severi himself in 1932, in which a gap was found afterwards. It is Pardini who finally gave a complete proof based on the covering trick and the slope inequality of Xiao. In 2009, Mendes Lopes and Pardini proposed a question about generalizing the classical Severi inequality to higher dimensions. In this talk, I will first introduce the classical Severi inequality and explain the above two ingredients in Pardini's proof. Then I will talk about a characteristic p>0 version of the Severi inequality which, a bit unexpectedly, gives a way to the Severi inequality in arbitrary dimension.