On regular non-cyclic covers of the projective line

Abstract: A regular cover of the projective line is a compact Riemann surface $S$ (or smooth projective algebraic curve) with action of a group $G$ in such a way that the corresponding quotient $S/G$ has genus zero. In this talk we shall consider those cases in which $G$ is non-cyclic and of order $pq$ where $p$ and $q$ are prime numbers. We shall discuss some recent results concerning the surfaces $S$ as before that form complex one-dimensional families in the moduli space of Riemann surfaces, and some related aspects concerning their Jacobian varieties.

Mathematics

Audience: researchers in the topic

Seminario de Geometría y Física - Matemática UCN-USP