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.
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