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Measures of Irrationality for Very General Abelian Varieties

Olivier Martin (Chicago University)

Aula Beltrami - Martedì 21 Maggio 2019 h.16:00


Abstract. Measures of Irrationality for Very General Abelian Varieties
Abstract: In recent years renewed attention has been brought to measures
of irrationality for projective varieties. While vector bundle methods
have been leveraged by Bastianelli, de Poi, Ein, Lazarsfeld, and Ullery
to study the degree of irrationality and covering gonality of high
degree hypersurfaces, building on work of Pirola and Alzati-Pirola,
Voisin has used rational equivalence of zero-cycles to show that the
covering gonality of a very general abelian variety of dimension g goes
to infinity with g. I will sketch how one can generalize Voisin's method
in order to prove the following conjecture: A very general abelian
variety of dimension at least 2k-1 has covering gonality greater than k.
If time permits, I will present new lower bounds on the degree of
(uni)irrationality of very general abelian varieties obtained in
collaboration with Colombo, Naranjo, and Pirola.

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