Deformation theory of orthogonal and symplectic sheaves

TL;DR

This paper develops a deformation and obstruction theory for orthogonal and symplectic sheaves on smooth projective schemes, characterizing their first-order deformations via hypercohomology of a naturally constructed complex.

Contribution

It introduces a novel hypercohomology-based framework for understanding deformations and obstructions of orthogonal and symplectic sheaves.

Findings

First-order deformation space described by first hypercohomology

Obstruction theory formulated via second hypercohomology

Provides a natural complex associated with these sheaves

Abstract

We show that the space of first-order deformations of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme is 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.