Frobenius map for quintic threefolds

2008/09/22 by I. Shapiro, Ilya Shapiro, Shapiro, I. · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.0809.3742

19 pages, discussion of $p$-adic zeta values added

openalex publication_date 2008/09/22 · arxiv created 2008/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate the matrix of the Frobenius map on the middle dimensional cohomology of the one parameter family that is related by mirror symmetry to the family of all quintic threefolds.

Citations

• Integrality of instanton numbers

Cited by

• Frobenius map on local Calabi–Yau manifolds
• Arithmetic geometry of quantum connections on Calabi-Yau 3-folds

Related

• Mirror Quintics, discrete symmetries and Shioda Maps
• The mirror formula for quintic threefolds
• Special geometry on the 101 dimesional moduli space of the quintic threefold
• Three constructions of Frobenius manifolds: a comparative study
• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds