2006/03/31 by Maxim Kontsevich, Albert Schwarz, Vadim Vologodsky · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.AG #math.NT
paper · pdf · doi:10.1016/j.physletb.2006.04.012
published as Phys.Lett.B637:97-101,2006 · 10 pages, minor changes
arxiv created 2006/04/09 · arxiv updated 2009/12/01
We study integrality of instanton numbers (genus zero Gopakumar - Vafa invariants) for quintic and other Calabi-Yau manifolds. We start with the analysis of the case when the moduli space of complex structures is one-dimensional; later we show that our methods can be used to prove integrality in general case. We give an expression of instanton numbers in terms of Frobenius map on p-adic cohomology ; the proof of integrality is based on this expression.