The relative irregularity of a fibration in plane quintics

19 dicembre 2017
19 dicembre 2017
Contatti: 
Staff Dipartimento di Matematica

Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"
Ore: 10.00

Relatore:

  • Filippo Favale

Abstract:

The relative irregularity of a fibration f:S->B is defined to be the difference between the irregularity of S and the genus of the base B.
What we call nowadays "Xiao's Conjecture" (a slight modification of the original conjecture of Xiao) predicts a non trivial bound for non isotrivial fibrations.
Although the conjecture is known to be true in some cases, 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 first open cases: fibrations whose general fiber is a plane quintic curve.

Referente: Claudio Fontanari