Slope inequalities for families of complete intersections

Department's Seminar
12 May 2023
Start time 
12:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room 1 (Povo 0)
Department of Mathematics
Target audience: 
University community
UniTrento students
Contact person: 
Roberto Pignatelli, Elisa Postinghel, Luis E. Solá Conde
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
Lidia Stoppino (University of Pavia)


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

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