On quantum cohomology ring of elliptic ℙ¹ orbifolds

2014/05/21 by Hansol Hong, Hong, Hansol, Hyung-Seok Shin +1
Mathematics · #11D45 #53D45 #57R18 #FOS: Mathematics #Number Theory (math.NT) #Symplectic Geometry (math.SG) #math.NT #math.SG #msc:11D45 #msc:53D45 #msc:57R18

paper · pdf · doi:10.48550/arxiv.1405.5344

37 pages, 11 figures, comments are welcome, v2: change in introduction

arxiv created 2014/06/15 · arxiv updated 2014/06/17

Abstract

We compute quantum cohomology ring of elliptic ℙ¹ orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-curves with certain orbifold coverings. The countings of orbi-curves are related to the integer solutions of Diophantine equations. This reproduces the computation of Satake and Takahashi in the case of ℙ¹_3,3,3 via different method.

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