Reza Seyyedali, Pure Mathematics Department, University of Waterloo
“Balanced metrics on ruled manifolds”
In 2001, Donaldson proved that the existence of cscK metrics on a polarized manifold (X,L) with discrete automorphism group implies existence of balanced metrics on Lk for k large enough. We show that a similar statement holds if one twists the line bundle L with a simple stable vector bundle E. More precisely we show that if E is a simple stable bundle over a polarized manifold (X,L), (X,L) admits cscK metric and has discrete automorphism group, then (PE∗,O(d)⊗Lk) admits balanced metric for k large enough.