Compactified moduli of projective bundles

Lieblich, Max

doi:10.2140/ant.2009.3.653

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Compactified moduli of projective bundles

Max Lieblich

Vol. 3 (2009), No. 6, 653–695

DOI: 10.2140/ant.2009.3.653

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

Mathematical Subject Classification 2000

Primary: 14D20

Secondary: 14D15

Milestones

Received: 19 October 2008

Revised: 24 May 2009

Accepted: 25 June 2009

Published: 20 November 2009

Authors

Max Lieblich
Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544-1000 United States	Department of Mathematics University of Washington Box 354350 Seattle, WA 98195 United States

Vol. 3, No. 6, 2009