Geometry Seminar

University of Tor Vergata, Department of Mathematics

13rd of December 2022, 14:30-15:30, room “Dal Passo”

Speaker

Lidia Stoppino

(Università di Pavia)

Title

On the slope of fibred surfaces 

Abstract

Let f be a surjective morphism with connected fibres from a projective smooth surface S to a projective smooth curve B, with genus of the general fibre F g>= 2. Let us suppose that f is not isotrivial (i.e. the smooth fibres are not mutally isomorphic) and that it is relatively minimal (i.e. the relative canonical divisor K_S-f^*K_B=K_f is realtively nef). The slope of f , called s(f), is defined to be the ratio between {K_f}^2 and the relative Euler characteristic \chi_f.

In this talk I will review old an new results on the serach of lower bounds for the slope, and I will discuss the methods used for this results, which are due to (in chronological order) Xiao, Cornalba-Harris, Moriwaki, Konno and Lu-Zuo.

Eventually I will discuss a recent result obatained in collaboration with a Ph.D. student of mine, Enea Riva, alongside with some possible strategy to improve these results.