Manuscripta Mathematica

, Volume 142, Issue 1–2, pp 1–34 | Cite as

Exceptional sequences on rational \({\mathbb{C}^{*}}\) -surfaces

  • Andreas HocheneggerEmail author
  • Nathan Owen Ilten


Inspired by Bondal’s conjecture, we study the behavior of exceptional sequences of line bundles on rational \({\mathbb{C}^{*}}\) -surfaces under homogeneous degenerations. In particular, we provide a sufficient criterion for such a sequence to remain exceptional under a given degeneration. We apply our results to show that, for toric surfaces of Picard rank 3 or 4, all full exceptional sequences of line bundles may be constructed via augmentation. We also discuss how our techniques may be used to construct noncommutative deformations of derived categories.

Mathematics Subject Classification (2010)

Primary: 14M25 14F05 Secondary: 14D06 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnCologneGermany
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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