Mirror Symmetry for hyperkaehler manifolds

Details Mirror Symmetry for hyperkaehler manifolds Mirror Symmetry for hyperkaehler manifolds

1995-12-24

arxiv.org/abs/hep-th/9512195v2

AMS/IP Stud. Adv. Math. 10 (1999) 115-156

Physics

High Energy Physics

High Energy Physics - Theory

62 pages, LaTeX 2e, minor corrections (grammar and typos) added since then

Scientific paper

We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a holomorphic symplectic form. Such manifolda are also known as complex manifolds of hyperkaehler type. We obtain that a complex manifold of hyperkaehler type is Mirror dual to itself. The Mirror Conjecture is stated (following Kontsevich, ICM talk) as the equivalence of certain algebraic structures related to variations of Hodge structures. We compute the canonical flat coordinates on the moduli space of Calabi-Yau manifolds of hyperkaehler type, introduced to Mirror Symmetry by Bershadsky, Cecotti, Ooguri and Vafa.

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