Restrictions on the Singularity Content of a Fano Polygon

2018/08/20 by Daniel Cavey, Cavey, Daniel · 1 voice
Mathematics · #14J45 #52B20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J45 #msc:52B20

paper · pdf · doi:10.48550/arxiv.1808.06476

14 pages, 3 figures

arxiv created 2018/08/20 · arxiv published 2018/08/20 · arxiv updated 2018/08/21

Abstract

We determine restrictions on the singularity content of a Fano polygon, or equivalently of certain orbifold del Pezzo surfaces. We establish bounds on the maximum number of 1/R(1,1) singularities in the basket of residual singularities. In particular, there are no Fano polygons without T-singularities and with a basket given by (i) k x 1/R(1,1) where k is a positive integer and R>4, or (ii) 1/R1(1,1), 1/R2(1,1), 1/R3(1,1).

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