Does anyone know a good reference to understand the historical background of Castelnuovo-Mumford regularity?
I know the backgound for the modern commutative-algebra approach (using free graded resolutions and Betti numbers) but I'd like to know the geometric motivations that led to the sheaf cohomology definition of $m$-regular sheaf.
Mumford, in his Lectures on curves on an algebraic surface and in a later article ascribes the definition of regular sheaves to Castelnuovo. I'd like to deepen in this way.