Classification of incidence scrolls. I. (Q5947083)

The authors define an incidence scroll in complex projective space as a ruled surface (a fibered surface over a curve whose fibers are isomorphic to \({\mathbb{P}}^1\) and which admits a global section) whose fibers meet a certain set of linear spaces in \({\mathbb{P}}^n\). Alternatively, a scroll is an incidence scroll if the corresponding curve in the Grassmann space \(G(1,n)\) is the intersection of special Schubert varieties. The authors give a complete classification of these scrolls if the genus of the base curve is \(0\) or \(1\). They promise an investigation of the general case. On the way, the authors obtain a number of interesting results, in particular about rational scrolls.