Deformation theory of orthogonal and symplectic sheaves

Abstract

We show that the deformation functor of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme admits a miniversal pro-family, identifying its space of first-order deformations with the first hypercohomology space of a complex which is naturally constructed out of the orthogonal (resp. symplectic) sheaf. We also provide an obstruction theory of these objects whose target is the second hypercohomology space of this complex.