Compactified moduli of projective bundles

Details Compactified moduli of projective bundles Compactified moduli of projective bundles

2007-06-11

arxiv.org/abs/0706.1311v4

Mathematics

Algebraic Geometry

28 pages. Major reogranization and clarification. Hypothesis removed; results as stated now apply to arbitrary stable bundles,

Scientific paper

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.

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