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26 April 2024
 
  » arxiv » 1501.5335

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Minimality and mutation-equivalence of polygons
Alexander Kasprzyk ; Benjamin Nill ; Thomas Prince ;
Date 21 Jan 2015
AbstractWe introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine the mutation-equivalence classes of such polygons. This is a key step in a program to classify orbifold del Pezzo surfaces using mirror symmetry. As an application, we classify all Fano polygons such that the corresponding toric surface is qG-deformation-equivalent to either (i) a smooth surface; or (ii) a surface with only singularities of type 1/3(1,1).
Source arXiv, 1501.5335
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