Exceptional collections of line bundles on projective homogeneous varieties期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Exceptional collections of line bundles on projective homogeneous varieties

Authors:	Alexey Ananyevskiy Asher Auel Skip Garibaldi Kirill Zainoulline

Institution:	1. Department of Mathematics and Mechanics, St. Petersburg State University, Universitetsky Prospekt 28, St. Petersburg, 198504, Russia;2. Department of Mathematics & Computer Science, Emory University, Atlanta, GA 30307, USA;3. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa ON K1N6N5, Canada

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 $G$ of rank 2 over a field. We exhibit exceptional collections of the expected length for types _A₂ $A_{2}$ and _B₂=_C₂ $B_{2} = C_{2}$ and prove that no such collection exists for type _G₂ $G_{2}$ . This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous G $G$ -varieties for split linear algebraic groups G $G$ of rank at most 2.

Keywords:	14F05 13D15 14M15 17B22 20G15
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