, Volume 142, Issue 1-2, pp 1-34
Date: 02 Nov 2012

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

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Abstract

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.