Exceptional Sequences on Rational C*-Surfaces

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.

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

References in corpus (5)

• Normal singularities with torus actions
• Polarized Complexity-One T-Varieties
• Examples for exceptional sequences of invertible sheaves on rational surfaces
• Families of Invariant Divisors on Rational Complexity-One T-Varieties
• Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example

Cited by in corpus (4)

• Families of Invariant Divisors on Rational Complexity-One T-Varieties
• Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example
• On cyclic strong exceptional collections of line bundles on surfaces
• Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two