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Exceptional sequences of invertible sheaves on rational surfaces

Part of:(Co)homology theoryAbelian categoriesSurfaces and higher-dimensional varietiesSpecial varieties

Published online by Cambridge University Press:  18 March 2011

Lutz Hille and
Markus Perling
Lutz Hille
Affiliation:
Mathematisches Institut, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstraße 62, 48149 Münster, Germany (email: lhill_01@uni-muenster.de)
Markus Perling
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany (email: Markus.Perling@rub.de)
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Abstract

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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.

Keywords

toric surfacesrational surfacesderived categoriesexceptional sequences

MSC classification

Secondary:14J26: Rational and ruled surfaces14M25: Toric varieties, Newton polyhedra18E30: Derived categories, triangulated categories14F05: Sheaves, derived categories of sheaves and related constructions

Information

Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011, pp. 1230 - 1280
Copyright
Copyright © Foundation Compositio Mathematica 2011

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