Splitting Problem for Homogeneous Supermanifolds

GAP Seminar

Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stienon, Ping Xu.

Speaker: Elizaveta Vishnyakova, University of Luxembourg

Abstract: A supermanifold is called split if it is isomorphic to a vector bundle with a purely even base and purely odd fiber. In the smooth category, all supermanifolds are known to be split (although non-canonically). In contrast, complex-analytic supermanifolds are not necessarily split, see for example the moduli space of super Riemann surfaces of genus $g>4$ (R.Donagi and E.Witten). The talk is devoted to the splitting problem for complex homogeneous spaces. While any complex Lie supergroup G is split, there are examples of non-split complex homogeneous supermanifolds. In fact, almost all flag supermanifolds are non-split. The main question that we will discuss is how to determine if a given complex homogeneous supermanifold is split or non-split. Our results will be illustrated on super Grassmannians.

Room Reservation Information

Room Number: 106 McAllister

Date: 12/10/2013

Time: 2:30pm - 3:30pm