Artal Bartolo (Zaragoza)

Title: Cyclotomic Zariski tuples with abelian fundamental group. 
From the pair to the complement.

Abstract: 
We define some reducible combinatorics of curves which produce Zariski tuples. 
These curves are a particular case of a family of curves defined by T. Shirane. 
Any of his curves can be degenerated to one of our case, 
and we prove that up to 2 exceptions their fundamental group are abelian. 
Using Cremona transformations, we will exhibit some candidates of irreducible 
combinatorics which are candidate to produce Zariski tuples. 
Finally, while the invariants we use are invariants of the pairs, 
we will explain how to derive that the complements are not homeomorphic. 
The first part of the work is a common work with J.I. Cogolludo and J. Martin-Morales, 
while the second one is a work in progress with S. Bannai, T. Shirane and H. Tokunaga.