Local Mirror Symmetry and Type IIA Monodromy of Calabi-Yau manifolds

2000/07/31 by S. Hosono
Physics and Astronomy · Mathematics · #hep-th #math.AG

paper · pdf

published as Adv.Theor.Math.Phys. 4 (2000) 335-376 · 30 pages, harvmac.tex; typos corrected, published version in Adv. Theor. Math. Phys. 4(2000)

arxiv created 2000/10/20 · arxiv updated 2009/11/30

Abstract

We propose a monodromy invariant pairing K_hol(X) ⊗ H₃(X^\vee,\ZZ) → \IQ for a mirror pair of Calabi-Yau manifolds, (X,X^\vee). This pairing is utilized implicitly in the previous calculations of the prepotentials for Gromov-Witten invariants. After identifying the pairing explicitly we interpret some hypergeometric series from the viewpoint of homological mirror symmetry due to Kontsevich. Also we consider the local mirror symmetry limit to del Pezzo surfaces in Calabi-Yau 3-folds.

Related

• Intrinsic mirror symmetry and punctured Gromov-Witten invariants
• Local Calabi-Yau manifolds of type A via SYZ mirror symmetry
• Families of Calabi-Yau manifolds and mirror symmetry
• Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers
• Local Mirror Symmetry: Calculations and Interpretations