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.
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Hochenegger, A., Ilten, N.O. Exceptional sequences on rational \({\mathbb{C}^{*}}\) -surfaces. manuscripta math. 142, 1–34 (2013). https://doi.org/10.1007/s00229-012-0591-9
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DOI: https://doi.org/10.1007/s00229-012-0591-9