On plane sextics with double singular points

We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.Comment: A few explanations and references adde

Projective spaces in Fermat varieties

We give a brief systematic overview of a few results concerning the N\'eron--Severi lattices of Fermat varieties and Delsarte surfaces

On the Picard group of a Delsarte surface

We suggest an algorithm computing, in some cases, an explicit generating set for the N\'eron--Severi lattice of a Delsarte surface

Zariski kk-plets via dessins d'enfants

We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.Comment: Final version accepted for publicatio