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arXiv · 1207.3334

Exceptional collections of line bundles on projective homogeneous varieties

Alexey Ananyevskiy·Asher Auel·Skip Garibaldi·Kirill Zainoulline
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Abstract

We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group G of rank 2 over a field. We exhibit exceptional collections of the expected length for types A_2 and B_2=C_2 and prove that no such collection exists for type G_2. This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous G-varieties for split linear algebraic groups G of rank at most 2.

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Alexey Ananyevskiy, Asher Auel, Skip Garibaldi, Kirill Zainoulline. 2012-07-13. Exceptional collections of line bundles on projective homogeneous varieties. https://doi.org/10.1016/j.aim.2012.12.016

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