Abstract:
We introduce and study 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 of the coverings and fixed ramification type.
As an application, we give new conditions on the ramification type that are
sufficient for the irreducibility of the Hurwitz spaces, suggest some bounds
on the number of irreducible components under certain more general
conditions, and show that the number of irreducible components coincides
with the number of topological classes of the coverings if the number
of branch points is big enough.
Keywords:irreducible components of the Hurwitz space of finite-sheeted coverings
of projective curves, semigroups over groups.