Combinatorial aspects of exceptional sequences on (rational) surfaces

Perling, Markus

doi:10.1007/s00209-017-1887-y

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Combinatorial aspects of exceptional sequences on (rational) surfaces

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Perling, Markus
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00209-017-1887-y
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Perling, M. (2018). Combinatorial aspects of exceptional sequences on (rational) surfaces. Mathematische Zeitschrift, 288(1-2), 243-286. doi:10.1007/s00209-017-1887-y.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6375-9

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.