Exceptional Sequences on Rational C*-Surfaces
Algebraic Geometry
2018-01-17 v2
Abstract
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.
Cite
@article{arxiv.1106.4743,
title = {Exceptional Sequences on Rational C*-Surfaces},
author = {Andreas Hochenegger and Nathan Owen Ilten},
journal= {arXiv preprint arXiv:1106.4743},
year = {2018}
}
Comments
30 pages, 11 figures. Some parts of this preprint originally appeared in arXiv:0906.4292v2 but have been revised and expanded upon. Minor changes, to appear in Manuscripta Mathematica