Slope inequalities for families of complete intersections

Abstract

Since the seminal papers of Xiao and Cornalba-Harris on fibred surfaces in the ’80s, slope inequalities have been a central problem in algebraic geometry, leading both to geographical results on the invariants of varieties, and to results about the positive cones of divisors of certain moduli spaces. 
I will describe the problem in general, the Cornalba-Harris approach (and its limits), and some recent results obtained in collaboration with Miguel Angel Barja, regarding the slope of fibrations whose general fibres are complete intersections. In particular, we prove the full slope inequality in any dimension for families whose general fibre is a local complete intersection of stable (e.g. smooth) hypersurfaces. 
Eventually, if time permits, I will describe also a way of finding, in the particular case of a family which is a global complete intersection, an instability result for the fibres.

Past events

Please have a look on the page of past seminars