In this work we review some papers by Corrado Segre published during the eighties of the XIX century, when he was just above twenty. We believe that doing so may be interesting from the historical point of view as well as helpful to recognizing a link between methods of research used in those years (scarcely present in contemporary literature) and a number of results rediscovered (often without knowing it) in the current century. We thus try to reconstruct the origin of the path that has led to the modern theory of vector bundles on an algebraic curve.

Corrado Segre's programme

To appreciate the innovative character of the ideas put forward by the very young Segre, it is convenient to recall that in those years it was harshly debated upon the usefulness of studying Hyperspace Geometry. Some authors mantained that addressing the geometry of the hyperspaces was an unfruitful intellectual game not certainly helpful to understand the “real” geometry in two or three dimensions. On the other side, Veronese and Bertini at first, and then C. Segre were perfectly aware that not only the study of the geometry of hyperspaces would shed new light on the geometry of curves and surfaces of ordinary space, but also that these latter could be viewed – and this is certainly innovative – as points (defined by a number of parameters) belonging to new algebraic varieties that could not be placed in ordinary space.