Seminar by Prof. Fabrizio Catanese on July 6th 2022

[Fabio Perroni]

Dear Colleagues, 

unfortunately, due to the flying chaos of these days, the seminar below is cancelled, it will be postponed to a later date.
I apologize for the inconvenience. 

Best regards,
Fabio Perroni

> Il giorno 30 giu 2022, alle ore 12:44, Fabio Perroni <fperroni at units.it> ha scritto:
> 
> 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
>