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A Construction of Frobenius Manifolds with Logarithmic Poles and Applications

Abstract

A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a partial generalization of the reconstruction theorem of Kontsevich and Manin for projective smooth varieties with convergent Gromov-Witten potential. A second application is a construction of Frobenius manifolds out of a variation of polarized Hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled.

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Correspondence to Thomas Reichelt.

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Communicated by N. A. Nekrasov

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Reichelt, T. A Construction of Frobenius Manifolds with Logarithmic Poles and Applications. Commun. Math. Phys. 287, 1145–1187 (2009). https://doi.org/10.1007/s00220-008-0699-7

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Keywords

  • Manifold
  • Vector Bundle
  • Hodge Structure
  • Holomorphic Vector Bundle
  • Nilpotent Orbit