Search results for "Galois cohomology"
showing 3 items of 3 documents
Irreducible components of Hurwitz spaces parameterizing Galois coverings of curves of positive genus
2014
Let Y be a smooth, projective, irreducible complex curve. A G-covering p : C → Y is a Galois covering, where C is a smooth, projective, irreducible curve and an isomorphism G ∼ −→ Aut(C/Y ) is fixed. Two G-coverings are equivalent if there is a G-equivariant isomorphism between them. We are concerned with the Hurwitz spaces H n (Y ) and H G n (Y, y0). The first one parameterizes Gequivalence classes of G-coverings of Y branched in n points. The second one, given a point y0 ∈ Y , parameterizes G-equivalence classes of pairs [p : C → Y, z0], where p : C → Y is a G-covering unramified at y0 and z0 ∈ p (y0). When G = Sd one can equivalently consider coverings f : X → Y of degree d with full mon…
Hurwitz spaces of Galois coverings of P1, whose Galois groups are Weyl groups
2006
Abstract We prove the irreducibility of the Hurwitz spaces which parametrize equivalence classes of Galois coverings of P 1 , whose Galois group is an arbitrary Weyl group, and the local monodromies are reflections. This generalizes a classical theorem due to Luroth, Clebsch and Hurwitz.
Real structures on nilpotent orbit closures
2021
We determine the equivariant real structures on nilpotent orbits and the normalizations of their closures for the adjoint action of a complex semisimple algebraic group on its Lie algebra.