Compositio Mathematica

Research Article

Exceptional sequences of invertible sheaves on rational surfaces

Lutz Hillea1 and Markus Perlinga2

a1 Mathematisches Institut, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstraße 62, 48149 Münster, Germany (email: lhill_01@uni-muenster.de)

a2 Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany (email: Markus.Perling@rub.de)

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.

(Received December 08 2009)

(Accepted June 15 2010)

(Online publication March 18 2011)

2000 Mathematics Subject Classification

  • 14J26;
  • 14M25;
  • 18E30 (primary);
  • 14F05 (secondary)

Keywords

  • toric surfaces;
  • rational surfaces;
  • derived categories;
  • exceptional sequences