Geometry Seminar

University of Tor Vergata, Department of Mathematics

14th of February 2023, 14:30-15:30, room “Dal Passo”

Speaker

Eleonora Romano

(Università di Genova)

Title

Recent results on Fano varieties

Abstract

In this talk we present some recent results on complex

smooth Fano varieties. To this end, we first recall an invariant

introduced by Casagrande, called Lefschetz defect. We review the

literature to deduce that all Fano manifolds with Lefschetz defect

greater than three are well known. Then we focus on the case in which

the Lefschetz defect is equal to three, by discussing a structure

theorem for such varieties. As an application, we use this result to

classify all Fano 4-folds with Lefschetz defect equal to three: there

are 18 families, among which 14 are toric. This is a joint work with

C. Casagrande and S. Secci.