Gino Fano's late investigations on Fano-Enriques threefolds

This paper investigates Gino Fano’s contributions to the study and classification of a special class of three-dimensional algebraic varieties: the so-called Fano-Enriques three-folds (i.e. Fano threefolds whose general hyperplane section is an Enriques surface). We focus on his 1938 memoir with the aim of analysing it from an historical-critical perspective, also in the light of its quite limited reception at that time and the subsequent rediscovery in the 1980s. Besides the weak links with foreign mathematical traditions, we consider the positioning of Fano’s work in the Italian geometric context. Starting from this case-study, we discuss some distinctive features of the ‘late’ Italian School of algebraic geometry which, combined with a scenario of cultural autarky, determined its decline.