Exceptional Sequences of Invertible Sheaves on Rational Surfaces

Details Exceptional Sequences of Invertible Sheaves on Rational Surfaces Exceptional Sequences of Invertible Sheaves on Rational Surfaces

2008-10-10

arxiv.org/abs/0810.1936v2

Comp. Math. 147(4), 1230-1280, 2011

Mathematics

Algebraic Geometry

40 pages, 5 figures, requires packages ams*, enumerate, xy, geometry, minor changes

Scientific paper

In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.

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