Projective bundles over hyperkaehler manifolds and stability of Fourier-Mukai transform
Misha Verbitsky
TL;DR
This paper discusses the properties of projective bundles over hyperkähler manifolds and examines the stability of the Fourier-Mukai transform, but has been withdrawn due to errors in key propositions.
Contribution
The paper aimed to analyze the stability of Fourier-Mukai transforms on projective bundles over hyperkähler manifolds, but its main results are invalidated by identified errors.
Findings
Proposition 11.4 is false
Section 12 is false
Main statement holds only for bundles with SU(2)-invariant first Chern class
Abstract
Paper withdrawn due to errors (superseded by math.AG/0604303). Proposition 11.4 is false, Section 12 is false, and the main statement is true only for bundles with SU(2)-invariant.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Nonlinear Waves and Solitons