AAG Seminar: The signed Euler characteristic property
Speaker: Deepam Patel, Purdue University
Abstract: Let X be a smooth variety over a field k. Then X satisfies the signed Euler characteristic property if for any smooth subvariety Z of X, (-1)^{dim(Z)}\chi(Z) \geq 0. It is a classical result of Franecki-Kapranov that this is true for any semi-abelian variety over a field of char(k) = 0. We survey some recent results extending this to the case of positive characteristic and to the setting of modulii stacks of abelian varieties and modulii stack of curves. If there is time, I will explain how this property relates to generic vanishing. This is partially based on joint work with Donu Arapura.
Host: Matt Kerr