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TILTING CHAINS OF NEGATIVE CURVES ON RATIONAL SURFACES

Published online by Cambridge University Press:  20 December 2017

LUTZ HILLE
Affiliation:
Freie Universitat Berlin, Mathematik und Informatik, Arnimallee 3-5, Berlin 14195, Germany email lhill_01@uni-muenster.de
DAVID PLOOG
Affiliation:
Freie Universitat Berlin, Mathematik und Informatik, Arnimallee 3-5, Berlin 14195, Germany email dploog@math.fu-berlin.de

Abstract

We introduce the notion of exact tilting objects, which are partial tilting objects $T$ inducing an equivalence between the abelian category generated by $T$ and the category of modules over the endomorphism algebra of $T$. Given a chain of sufficiently negative rational curves on a rational surface, we construct an exceptional sequence whose universal extension is an exact tilting object. For a chain of $(-2)$-curves, we obtain an equivalence with modules over a well-known algebra.

Type
Article
Copyright
© 2017 Foundation Nagoya Mathematical Journal  

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