Geodesic
MINIMALITY AND MUTATION-EQUIVALENCE OF POLYGONS
Forum of Mathematics, Sigma, Tome 5 (2017)

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We 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 representatives for all 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 $1/3(1,1)$ . 
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     author = {ALEXANDER KASPRZYK and BENJAMIN NILL and THOMAS PRINCE},
     title = {MINIMALITY {AND} {MUTATION-EQUIVALENCE} {OF} {POLYGONS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {5},
     year = {2017},
     doi = {10.1017/fms.2017.10},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2017.10/}
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ALEXANDER KASPRZYK; BENJAMIN NILL; THOMAS PRINCE. MINIMALITY AND MUTATION-EQUIVALENCE OF POLYGONS. Forum of Mathematics, Sigma, Tome 5 (2017). doi: 10.1017/fms.2017.10

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