Vol. 3, No. 6, 2009

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Compactified moduli of projective bundles

Max Lieblich

Vol. 3 (2009), No. 6, 653–695
Abstract

We present a method for compactifying stacks of PGL${}_{n}$-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are irreducible and carry natural virtual fundamental classes. We also prove a version of the Skolem–Noether theorem for certain algebra objects in the derived category, which allows us to give an explicit description of the boundary points in our compactified moduli problem.

Keywords
projective bundles, moduli of stable bundles, Skolem–Noether theorem, derived categories, rigidification
Primary: 14D20
Secondary: 14D15