Title: Relative Clifford inequality, slope inequality and volume inequality

Speaker：张通教授 (华东师范大学)

Abstract:

In this talk, I will introduce a Clifford inequality for special divisors on "relative" curves, namely varieties fibered by curves. I will also talk about how to apply such an inequality to deduce a slope inequality for higher dimensional families of curves, as well as a volume inequality for "relative" curves over varieties of maximal Albanese dimension. These results extend the previous work of Cornalba, Harris, Horikawa, Persson and Xiao to higher dimensions.