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Toric systems and mirror symmetry

Part of: Surfaces and higher-dimensional varieties Special varieties

Published online by Cambridge University Press:  28 August 2013

Raf Bocklandt
Raf Bocklandt*
Affiliation:
School of Mathematics and Statistics, Herschel Building, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK email raf.bocklandt@gmail.com
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Abstract

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In their paper [Exceptional sequences of invertible sheaves on rational surfaces, Compositio Math. 147 (2011), 1230–1280], Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak del Pezzo surface a toric system, which defines a new toric surface. We interpret this construction as an instance of mirror symmetry and extend it to a duality on the set of toric weak del Pezzo surfaces equipped with a cyclic full strongly exceptional sequence.

Keywords

dimershelicesdel Pezzo surfacestoric systemshomological mirror symmetry

MSC classification

Secondary: 14M25: Toric varieties, Newton polyhedra 14J33: Mirror symmetry 14J45: Fano varieties 14J32: Calabi-Yau manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 11 , November 2013 , pp. 1839 - 1855
Copyright
© The Author(s) 2013 

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