Castelnuovo-Mumford Regularity and Splitting Criteria for Logarithmic Bundles over Rational Normal Scroll Surfaces

We introduce and study a notion of Castelnuovo-Mumford regularity suitable for rational normal scroll surfaces. In this setting we prove analogs of some classical properties. We prove splitting criteria for coherent sheaves and a characterization of Ulrich bundles. Finally we study logarithmic bundles associated to arrangements of lines and rational curves.