Seminário de Geometria Algébrica e Geometria Complexa – 06/10 – Yerika Marín e Pablo Quezada Mora – online

Caros colegas,

Seguem abaixo as informações dos nossos próximos dois Seminários de Geometria Algébrica e Geometria Complexa da UFF.

Para consultar os próximos seminários e o histórico, basta consultar o site do Grupo de Geometria Algébrica e Complexa da UFF:

https://sites.google.com/view/geoalgcompluff

Palestrante: Yerika Marín

Título: Generalized quasi-dihedral group acting on pseudo-real Riemann surfaces

Resumo: A closed Riemann surface of genus $g \geq 2$ is called pseudo-real if it has anticonformal automorphisms but no anticonformal involutions. These Riemann surfaces, together with real Riemann surfaces, form the real locus of the moduli space $\mathcal{M}_g$ of closed Riemann surfaces of genus $g \geq 2$ . On the other hand, pseudo-real Riemann surfaces are examples of Riemann surfaces which cannot be defined over their field of moduli [1]. In general, a finite group might not be realized as the group of conformal/anticonformal automorphisms, admitting anticonformal ones, of a pseudo-real Riemann surface, for instance, in [2], it was observed that a necessary condition for that to happen is for the group to have order a multiple of 4 . In this talk, we consider conformal/anticonformal actions of the generalized quasi-dihedral group of order $8 n$ ,
$G_n=\left\langle x, y: x^{4 n}=y^2=1, y x y=x^{2 n-1}\right\rangle \quad(\text { for } n \geq 2)$
on pseudo-real Riemann surfaces. We consider two cases either $G_n$ has anticonformal elements or $G_n$ only contains conformal elements [3].
This is part of my Ph.D. Thesis, under the advisers Saúl Quispe and Rubén A. Hidalgo.

References
[1] M. Artebani, S. Quispe and C. Reyes. Automorphism groups of pseudoreal Riemann surfaces Journal of Pure and Applied Algebra 221 (2017), 2383-2407.
[2] E. Bujalance, M. D. E. Conder and A. F. Costa. Pseudo-real Riemann surfaces and chira regular maps, Trans. Am. Math. Soc. 362 (7) (2010), 3365-3376.
[3] R. A. Hidalgo, Y. Marín Montilla and S. Quispe. Generalized quasi-dihedral group as automorphism group of Riemann surfaces, Preprint 2022.

Data: 06/10/2023 (Sexta-feira)

Horário: 15h

Link: https://meet.google.com/mnw-coar-fji

Palestrante: Pablo Quezada Mora

Título: IHS Manifolds of K3^[2]-type with an action of Z_3^4 : A_6

Resumo: In this talk we will study IHS manifolds of K3^[2]-type with a symplectic action of Z_3^4 : A_6, the symplectic group with the biggest order, and such that they also admit a non-symplectic automorphism. We will characterize the IHS manifolds that satisfies this, and particularly we will characterize the IHS manifold of K3^[2]-type with finite automorphism group of order 174960, the biggest possible order for the finite automorphism group of a IHS manifold of K3^[2]-type, and we will give an example of it. This is a joint work with Paola Comparin and Romain Demelle.

Data: 06/10/2023 (Sexta-feira)

Horário: 16h

Link: https://meet.google.com/mnw-coar-fji