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 obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis leads in some examples to a generically non-reduced component of the moduli space, and a component which is generically smooth of one bigger 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. 2009. ⟨hal-00414445v1⟩