Irrational pencils, and characterization of Varieties isogenous to a product, via the Profinite completion of the Fundamental group

Fabrizio Catanese, appendix by Pavel Zalesskii

We give a very short proof of two Theorems, whose content is outlined in the title, and where ${\Pi }_g$ is the fundamental group of a compact complex curve of genus $g$: (1) Theorem 2.…