Fonctionne avec Indico
v3.2.9
The relative irregularity of a fibration from a surface S to a curve B is defined to be the difference between the irregularity of S and the genus of B. What we call nowadays "Xiao's Conjecture" (a slight modification of the original conjecture of Xiao) predicts a sharp bound for the relative irregularity in terms of the genus of the generic fiber. The conjecture is known to be true in some cases but it is safe to say that is widely open. I will talk about some recent ideas in order to approach the conjecture in the cases where the genus of the general fiber is small. In particular, I will talk about a work in collaboration with J.C. Naranjo and G.P. Pirola in which we proved the conjecture for one of the open cases: fibrations whose general fiber is a plane quintic curve.