Mirror symmetry and $\mathbb {C}^\times $

DOI10.1090/S0002-9939-00-05901-3zbMath0967.14035arXivmath/0004178OpenAlexW2037942032MaRDI QIDQ4510044

Nobuyoshi Takahashi

Publication date: 19 October 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0004178

zbMATH Keywords

mirror symmetryelliptic curveCalabi-Yau manifoldnormal crossing divisorcompact Kähler manifoldcounting formulasimply ramified finite coverings

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Elliptic curves over global fields (11G05) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Elliptic curves (14H52) Coverings of curves, fundamental group (14H30) Symmetric groups (20B30)

Cites Work

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• Toda equations for Hurwitz numbers
• A proof of a conjecture for the number of ramified coverings of the sphere by the torus
• The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
• Log mirror symmetry and local mirror symmetry.

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