2013/12/15 by Michel van Garrel, van Garrel, Michel, Tony W. H. Wong +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1312.4112
15 pages, revised version
arxiv created 2014/04/14 · arxiv updated 2014/04/16
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert and conjectured by the authors to be integers. For toric Del Pezzo surfaces, we provide an arithmetic proof of this conjecture, by relating these invariants to the local BPS state counts of the surfaces. The latter were shown to be integers by Peng; and more generally for toric Calabi-Yau threefolds by Konishi.