Exceptional Sequences on Rational C*-Surfaces

Details Exceptional Sequences on Rational C*-Surfaces Exceptional Sequences on Rational C*-Surfaces

2011-06-23

arxiv.org/abs/1106.4743v1

Mathematics

Algebraic Geometry

30 pages, 11 figures. Some parts of this preprint originally appeared in arXiv:0906.4292v2 but have been revised and expanded

Scientific paper

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational 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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