On families of rank-2 uniform bundles on Hirzebruch surfaces and Hilbert schemes of their scrolls
arXiv:1501.06644
Abstract
Several families of rank-two vector bundles on Hirzebruch surfaces are shown to consist of all very ample, uniform bundles. Under suitable numerical assumptions, the projectivization of these bundles, embedded by their tautological line bundles as linear scrolls, are shown to correspond to smooth points of components of their Hilbert scheme, the latter having the expected dimension. If e=0,1 the scrolls fill up the entire component of the Hilbert scheme, while for e=2 the scrolls exhaust a subvariety of codimension 1.
12 pages; submitted pre-print; previous papers arXiv:1110.5464, for e=1, and arXiv:1406.0956, for any e, dealt with vector bundles having first Chern class which ensures that they are always uniform. This is not the case for the present paper