Using Bridgeland stability conditions, we give sufficient criteria for a stable vector bundle on a smooth complex projective surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the plane. As an application, we compute the cohomology of such bundles for curves that lie in the plane or on Hirzebruch surfaces.
"Stability Conditions for Restrictions of Vector Bundles on Projective Surfaces." Michigan Math. J. 69 (4) 711 - 732, October 2020. https://doi.org/10.1307/mmj/1592359275