Combinatorial aspects of exceptional sequences on (rational) surfaces

Article

Abstract

We investigate combinatorial aspects of exceptional sequences in the derived category of coherent sheaves on certain smooth and complete algebraic surfaces. We show that to any such sequence there is canonically associated a complete toric surface whose torus fixpoints are either smooth or cyclic T-singularities (in the sense of Wahl) of type \(\frac{1}{r^2}(1, kr - 1)\). We also show that any exceptional sequence can be transformed by mutation into an exceptional sequence which consists only of objects of rank one.

Mathematics Subject Classification

Primary 14F05 14J26 14M25 Secondary 14J29 32S25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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