Geometry Seminar

Moduli spaces of holomorphic differential forms on Riemann surfaces carry a natural GL(2,R)-action.
By recent breakthroughs orbit closures for this action are surprisingly well behaved: They are quasi-projective varieties that are locally defined by linear equations. Orbit closures are never compact and it is natural to search for "nice" compactifications. We explicitly construct an algebraic compactification and study the boundary of orbit closures. Our main result is an explicit description of the defining equations for the boundary. In particular the boundary is again given by linear equations. Time permitting, we explain how our description of the boundary can be used to extend Wrights cylinder deformation theorem to the case of meromorphic differential forms. Speaker(s): Frederik Benirschke (Stony Brook University)