Cari tutti,
Il prossimo seminario di geometria algebrica e aritmetica di Pisa si terrà (speriamolo) IN PRESENZA
il mercoledì 28 OTTOBRE 2020 in Aula Magna del Dipartimento
Prego i colleghi esterni al dipartimento di segnalarmi sel'hanno l'intenzione di venire (misure COVID...)
Migliori saluti, Tamás Szamuely
----------
Programma:
11:00--12:00 Davide Lombardo (Pisa): The modified Hilbert property for abelian varieties
In this talk I will present joint work with P. Corvaja, J. Demeio, A. Javanpeykar, and U. Zannier. We show that for every abelian variety A over a number field K having a Zariski dense subset A(K) of rational points, every ramified, irreducible cover X → A, and every subgroup Ω of A(K) that is Zariski dense in A, there is a finite-index coset of points of Ω that do not lift to K-points of X. This confirms a conjecture of Corvaja and Zannier concerning their "generalized Hilbert property" for rational points in the case of abelian varieties.
---------
14:30--15:30 Laura Pertusi (Milano): Elliptic quintics on cubic fourfolds, O'Grady 10 and Lagrangian fibrations
In this talk we study certain moduli spaces of semistable objects in the Kuznetsov component of a cubic fourfold. We show that they admit a symplectic resolution M˜ which is a smooth projective hyperkaehler manifold deformation equivalent to the 10-dimensional example constructed by O'Grady. As a first application, we construct a birational model of M˜ which is a compactification of the twisted intermediate Jacobian of the cubic fourfold. Secondly, we show that M˜ is the MRC quotient of the main component of the Hilbert scheme of elliptic quintic curves in the cubic fourfold, as conjectured by Castravet. This is a joint work with Chunyi Li and Xiaolei Zhao.