Seminar by Prof. Matteo Penegini

[Fabio Perroni]

UNIVERSITA’ DEGLI STUDI DI TRIESTE
DIPARTIMENTO DI MATEMATICA E GEOSCIENZE

SEMINAR ANNOUNCEMENT

Monday, April 8th, 2019, at 14:30.

Prof. Matteo Penegini (University of Genova) will speak on "Tate and Mumford--Tate conjecture for surfaces of general type with p_g=q=2”.

Abstract. In this talk we discuss the cohomology of smooth projective complex surfaces S
of general type with invariants p_g = q = 2 and surjective Albanese morphism.
We show that on a Hodge-theoretic level, the cohomology is described
by the cohomology of the Albanese variety and a K3~surface X  that we call the K3 partner of S.
Furthermore, we show that in suitable cases we can geometrically construct
the K3 partner X  and an algebraic correspondence in S \times X that relates the cohomology of S  and X .
Finally, we prove the Tate and Mumford--Tate conjectures for those surfaces S 
that lie in connected components of the Gieseker moduli space that contain a product-quotient surface.

Venue: Seminar Room  (Sezione di Matematica e Informatica, H2 building, Via Valerio 12/1, 3rd floor, room 334).

Everybody interested is much welcome to attend.
Best regards,
Fabio Perroni