[Dottorcomp] Seminari di Geometria e Algebra - 26 novembre 2025

[Lidia Stoppino]

Il giorno 26 novembre 

in Aula Beltrami 
alle ore 16,15 (durata 1 ora)

Davide Frapporti (Politecnico di Milano)
 
terrà un seminario dal titolo:
On numerically and cohomologically trivial automorphisms of surfaces

Abstract:  
For a compact complex manifold X, let Aut(X) be its group of automorphisms.
In the talk I will mainly consider two subgroups of Aut(X): Aut_Z(X) the subgroups of cohomologically trivial automorphisms, i.e. of those automorphisms acting trivially on the cohomology with integer coefficients H^*(X,Z); and the larger subgroup Aut_Q(X) of numerically trivial automorphisms, i.e. of those automorphisms acting trivially on the rational cohomology H^(X,Q). For curves, these 2 subgroups are easily described, but already for surfaces the situation is quite complicated. 
After recalling some known results, I will describe Aut_Z(X) and Aut_Q(X) for minimal surfaces with Kodaira dimension 1 and \chi(S) = 0 (joint work with F. Catanese, C. Gleißner, W. Liu and M. Schütt). These are surfaces isogenous to a higher elliptic product, i.e. free quotients (C x E)/G where E is an elliptic curve, C is a curve of genus ≥ 2 and G is a finite group acting diagonally.
In particular, I will show that in the pseudo-elliptic case (G acts by translations on E), Aut_Z(X)=E, or |Aut_Z(X)/E|=2; while, if G does not act by translations on E, then Aut_Z(X) is either cyclic of order at most 3, or the Klein group; and exhibit examples of the former cases. 
Finally, I will report on a work in progress with F. Catanese and describe Aut_Z(X) and Aut_Q(X) for  surfaces isogenous to a higher product with p_g=q=0. In particular, I will describe two surfaces: one having |Aut_Q(X)|=192, and another one with Aut_Z(X) of order 2.

Tutti gli interessati sono invitati a partecipare. 
Andremo a PRANZO allo Swimland partendo alle 13.00 dal dipartimento. Chi vuole venire scriva tempestivamente a me, a Filippo Favale <filippo.favale a unipv.it> e a Davide Bricalli <davide.bricalli a unipv.it>
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Lidia Stoppino
Dipartimento di Matematica
Università di Pavia
Via Ferrata 5
27100 Pavia
Ufficio C.07 (primo piano)
Tel. +39 0382 985624
e-mail: lidia.stoppino a unipv.it 
pagina web: http://www.stoppino.it