Vol. 3, No. 6, 2009

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Compactified moduli of projective bundles

Max Lieblich

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

We present a method for compactifying stacks of PGLn-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