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.
This publication is cited in the following 5 articles:
R. Moschetti, G. P. Pirola, “Hurwitz spaces and liftings to the Valentiner group”, J. Pure Appl. Algebra, 222:1 (2018), 19–38
V. I. Zvonilov, S. Yu. Orevkov, “Compactification of the Space of Branched Coverings of the Two-Dimensional Sphere”, Proc. Steklov Inst. Math., 298 (2017), 118–128
F. A. Bogomolov, Vik. S. Kulikov, “The ambiguity index of an equipped finite group”, Eur. J. Math., 1:2 (2015), 260–278
F. Catanese, “Topological methods in moduli theory”, Bull. Math. Sci., 5:3 (2015), 287–449
V. Kanev, “Irreducible components of Hurwitz spaces parameterizing Galois coverings of curves of positive genus”, Pure Appl. Math. Q., 10:2 (2014), 193–222
Citation in format AMSBIB
Contact us: