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Differential Graded Quivers of Smooth Rational Surfaces

Part of: Surfaces and higher-dimensional varieties Special varieties (Co)homology theory

Published online by Cambridge University Press:  15 December 2016

Agnieszka Bodzenta
Agnieszka Bodzenta*
Affiliation:
School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK ([email protected])
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Abstract

Let X be a smooth rational surface. We calculate a differential graded (DG) quiver of a full exceptional collection of line bundles on X obtained by an augmentation from a strong exceptional collection on the minimal model of X. In particular, we calculate canonical DG algebras of smooth toric surfaces.

Keywords

derived categoriesexceptional collectionsDG categorytoric varieties

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions 14J26: Rational and ruled surfaces 14M25: Toric varieties, Newton polyhedra
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 4 , November 2017 , pp. 859 - 876
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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