Michael Lönne

Irreducibility of the space of dihedral covers of the projective line of a given numerical type

We show in this paper that the set of irreducible components of the family of Galois coverings of P^1_C with Galois group isomorphic to D_n is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of D_n) of the function which to each conjugacy class \mathcal{C} in D_n associates the number of branch points whose local monodromy lies in the class \mathcal{C}.

The irreducible components of the moduli space of dihedral covers of algebraic curves

In this paper we introduce a new invariant for the action of a finite group

Moduli spaces and braid monodromy types of bidouble covers of the quadric

G

Presentations of subgroups of the braid group generated by powers of band generators

on a compact complex curve of genus

BRAID MONODROMY OF SOME BRIESKORN–PHAM SINGULARITIES

g

Bifurcation braid monodromy of plane curves

. With the aid of this invariant we achieve the classification of the components of the moduli space of curves with an effective action by the dihedral group

Fundamental group of discriminant complements of Brieskorn–Pham polynomials

D_n

Braid Monodromy of Hypersurface Singularities

. This invariant has been used in the meanwhile by the authors in order to extend the genus stabilization result of Livingston and Dunfield and Thurston to the ramified case. This new version contains an appendix clarifying the correspondence between the above components and the image loci in the moduli space M_g (classifying when two such components have the same image).

Genus stabilization for moduli of curves with symmetries

Bidouble covers

Moduli spaces of surfaces and monodromy invariants

\pi : S \mapsto Q