Basepoint freeness for nef and big line bundles in positive characteristic.
Basis of homology adapted to the trigonal automorphism of a Riemann surface.
A closed (compact without boundary) Riemann surface S of genus g is said to be trigonal if there is a three sheeted covering (a trigonal morphism) from S to the Riemann sphere, ƒ : S →Ĉ. If there is an automorphism of period three, φ, on S permuting the sheets of the covering, we shall call S cyclic trigonal and will be called trigonal automorphism. In this paper we determine the intersection matrix on the first homology group of a cyclic trigonal Riemann surface on an adapted basis B to the trigonal...
Belyi's theorem revisited.
Blaschke product generated covering surfaces
It is known that, under very general conditions, Blaschke products generate branched covering surfaces of the Riemann sphere. We are presenting here a method of finding fundamental domains of such coverings and we are studying the corresponding groups of covering transformations.
Braid Monodromy of Algebraic Curves
These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009.This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective curves.The main classical results are stated...
Branching data for algebraic functions and representability by radicals
The branching data of an algebraic function is a list of orders of local monodromies around branching points. We present branching data that ensure that the algebraic functions having them are representable by radicals. This paper is a review of recent work by the authors and of closely related classical work by Ritt.