# Combinatorial aspects of exceptional sequences on (rational) surfaces

Combinatorial aspects of exceptional sequences on (rational) surfaces 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 $$\frac{1}{r^2}(1, kr - 1)$$ 1 r 2 ( 1 , k r - 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

# Combinatorial aspects of exceptional sequences on (rational) surfaces

, Volume 288 (2) – May 10, 2017
44 pages

Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-017-1887-y
Publisher site
See Article on Publisher Site

### 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 $$\frac{1}{r^2}(1, kr - 1)$$ 1 r 2 ( 1 , k r - 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.

### Journal

Mathematische ZeitschriftSpringer Journals

Published: May 10, 2017

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