Seminar by Prof. Fabrizio Catanese on July 6th 2022

[Fabio Perroni]

UNIVERSITA’ DEGLI STUDI DI TRIESTE
DIPARTIMENTO DI MATEMATICA E GEOSCIENZE

SEMINAR ANNOUNCEMENT

Wednesday, July 6, 2022, at 11:30.

Prof. Fabrizio Catanese (University of Bayreuth) will give a seminar on "MANIFOLDS WITH VANISHING CHERN CLASSES AND SOME QUESTIONS BY SEVERI/BALDASSARRI”.

Abstract: We give a negative answer to a question posed by Severi in 1951, whether the Abelian Varieties are the only manifolds with vanishing Chern classes. 
We exhibit Hyperelliptic Manifolds which are not Abelian varieties (nor complex tori) and whose Chern classes are zero not only in integral homology, but also in the Chow ring.
We prove moreover that the Bagnera de Franchis manifolds ( T/G where G is cyclic) have topologically trivial tangent bundle. 
Motivated by a more general question addressed by Mario Baldassarri in 1956, we discuss the Hyperelliptic Manifolds, the Pseudo-Abelian Varieties introduced by Roth, 
and we introduce a new notion, of Manifolds Isogenous to a k-Torus Product: the latter have the last k Chern classes trivial in rational homology and vanishing Chern numbers. 
We show that the latter class is the correct substitute for some incorrect assertions by Enriques, Dantoni, Roth and Baldassarri: in dimension 2 these are the surfaces with KX nef and c2(X) = 0.
A  similar picture  does not hold  in higher dimension, unless we consider  manifolds (isogenous to manifolds) whose tangent (resp. cotangent bundle) has a trivial summand, and related results and open problems.

Venue:  the seminar will take place at the Seminar Room of the Department (Sezione di Matematica e Informatica, H2 building, Via Valerio 12/1, 3rd floor, room 334).


Everyone interested is welcome to attend.
Best regards,
Fabio Perroni