Back to Algebraic Geometry Seminar: Spring 2026
Algebraic Geometry Seminar
Date: Tuesday, Feb 17, 2026
Time: 3:30PM - 4:30PM
Location: LCB 215
Marta Benozzo
Universite Paris-Saclay
Title |
On the canonical bundle formula in positive characteristic |
Abstract |
An important problem in birational geometry is trying to relate in a meaningful way the canonical bundles of the source and the base of a fibration. The first instance of such a formula is Kodaira’s canonical bundle formula for surfaces which admit a fibration with elliptic fibres. It describes the relation between the canonical bundles in terms of the singularities of the fibres and their j-invariants. In higher dimension, we do not have an equivalent of the j-invariant, but we can still define a moduli part. Over fields of characteristic 0, positivity properties of the moduli part have been studied using variations of Hodge structures. Recently, the problem has been addressed with the minimal model program for foliations, which is known to fail in positive characteristic. In this talk I will explain an approach to the canonical bundle formula which adapts these methods in positive characteristic. |
Algebraic Geometry