Frobenius Modules and Hodge Asymptotics

2002/07/31 by Eduardo Cattani, Javier Fernández, Javier Fernandez · 6 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Mathematics #Pure mathematics #math.AG #msc:14D07 #msc:14J32 #msc:14N35 #msc:32G20

paper · pdf · doi:10.1007/s00220-003-0848-y

published in Communications in Mathematical Physics 238(3), 489-504 (Springer Science+Business Media) · Updated bibliography. Final version published in Commun. Math. Phys

openalex publication_date 2003/07/01 · arxiv created 2003/07/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We exhibit a direct correspondence between the potential defining the H^1,1 small quantum module structure on the cohomology of a Calabi-Yau manifold and the asymptotic data of the A-model variation of Hodge structure. This is done in the abstract context of polarized variations of Hodge structure and Frobenius modules.

Citations

• String Theory on Calabi-Yau Manifolds
• Picard-Fuchs equations and mirror maps for hypersurfaces
• Mirror Symmetry and Algebraic Geometry
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
• Periods of Integrals on Algebraic Manifolds, I. (Construction and Properties of the Modular Varieties)