Publisher： Cambridge University Press
E-ISSN： 1570-5846|147|4|1230-1280
ISSN： 0010-437x
Source： Compositio Mathematica, Vol.147, Iss.4, 2011-07, pp. : 1230-1280
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Abstract
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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