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Exceptional sequences of invertible sheaves on rational surfaces

  • Lutz Hille (a1) and Markus Perling (a2)
  • DOI: http://dx.doi.org/10.1112/S0010437X10005208
  • Published online: 18 March 2011
Abstract
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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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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