Geometry and Analysis Seminar

Weighted flag varieties are generalizations of flag varieties and weighted projective spaces.  Although they are not usually homogeneous varieties, they are orbifolds and admit a torus action with isolated fixed points, and like ordinary flag varieties, their equivariant cohomology admits a Schubert basis.  This talk will be an introduction to weighted flag varieties, and will also discuss positivity.  Abe and Matsumura proved that the equivariant cohomology of weighted Grassmannians has a positivity property analogous to that for ordinary (non-weighted) flag varieties.  We prove a strengthened version of this result for arbitrary weighted flag varieties, along the way providing a geometric interpretation of the weighted roots of Abe and Matsumura.  This is joint work with Scott Larson.