Open Access
2009 Compactified moduli of projective bundles
Max Lieblich
Algebra Number Theory 3(6): 653-695 (2009). DOI: 10.2140/ant.2009.3.653


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.


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Max Lieblich. "Compactified moduli of projective bundles." Algebra Number Theory 3 (6) 653 - 695, 2009.


Received: 19 October 2008; Revised: 24 May 2009; Accepted: 25 June 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1195.14016
MathSciNet: MR2579390
Digital Object Identifier: 10.2140/ant.2009.3.653

Primary: 14D20
Secondary: 14D15

Keywords: derived categories , moduli of stable bundles , projective bundles , rigidification , Skolem–Noether theorem

Rights: Copyright © 2009 Mathematical Sciences Publishers

Vol.3 • No. 6 • 2009
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