Seminar in Real & Complex Geometry

Tuesday, 8.05.2012, 15:00-16:30, Schreiber building, room 210

Victor Kulikov, Steklov Mathematical Institute

Covering Semigroups


A semigroup structure on the set of irreducible components of the Hurwitz space of marked coverings of a complex projective curve with given Galois group and fixed ramification type will be introduced. As application, we find new restrictions on the ramification type that are sufficient for the irreducibility of Hurwitz spaces, suggest some bounds on the number of irreducible components under certain more general conditions, and show that under some stability assumptions on the ramification type, the number of irreducible components coincides with the number of topological classes of coverings.