Irreducibility of the Set of All Two-Dimensional Scrolls with very Few Sections

Keywords:

scroll, surface scroll, rank two vector bundle, ruled surface, Petri curve coherent system,

[1] Bradlow, S. B., Garc´ıa Prada, V. Mun˜oz, V. and Newstead, P. E., Coherent systems and Brill-Noether theory, Internat. J. Math., 14 (2003), no. 7, 683–773.
[2] Calabri, A., Ciliberto, C., Flamini, F. and Miranda, R., Degenerations of scrolls to unions of planes, Rend. Lincei Mat. Appl., (IX) 17 (2006), no. 2, 95–123.
[3] Calabri, A., Ciliberto, C., Flamini, F. and Miranda, R., Non-special scrolls with general moduli, Rend. Circ. Mat. Palermo, (2) 57 (2008), no. 1, 1–31.
[4] Teixidor i Bigas, M., Existence of vector bundles of rank two with sections, Adv. Geom., 5 (2005), no. 1, 37–47.