Obstructed bundles of rank two on a quintic surface

Nicole Mestrano (1) , Carlos Simpson (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis leads to generically non-reduced components of the moduli space, and components which are generically smooth of more than the expected dimension. We obtain a sharp bound asked for by O'Grady saying when the moduli space is good.

Domaines: Géométrie algébrique [math.AG]

Nicole Mestrano, Carlos Simpson. Obstructed bundles of rank two on a quintic surface. International Journal of Mathematics, 2011, 22 (6), pp.789-836. ⟨10.1142/S0129167X11007045⟩. ⟨hal-00414445v4⟩