a1 Mathematisches Institut, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstraße 62, 48149 Münster, Germany (email: firstname.lastname@example.org)
a2 Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany (email: Markus.Perling@rub.de)
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.
(Received December 08 2009)
(Accepted June 15 2010)
(Online publication March 18 2011)
2000 Mathematics Subject Classification