Deformation theory for orthogonal and symplectic sheaves

Abstract: Moduli spaces of principal bundles usually carry interesting geometric structures, being a powerful, and often unique, source of examples of varieties with prescribed properties and characteristics. Nevertheless, these spaces might be non-compact whenever the base (smooth) scheme has dimension higher than 1. Principal sheaves provide a natural compactification of the moduli space of principal bundles for a connected complex reductive structure group. Therefore, moduli spaces of principal sheaves are projective varieties equipped with an interesting geometry, at least, on a dense subset. In order to check whether or not these properties extend to the compactification, we need a local description of the moduli spaces, precisely over the locus where the principal sheaves fail to be principal bundles. Such description would naturally derive from deformation theory of principal sheaves, which is still missing at present date.

In this talk we consider orthogonal and symplectic sheaves, and show that the deformation and obstruction theory of these objects is controlled by a deformation complex naturally built out of our starting orthogonal (resp. symplectic) sheaf.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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