A construction of Frobenius manifolds with logarithmic poles and applications

Details A construction of Frobenius manifolds with logarithmic poles and applications A construction of Frobenius manifolds with logarithmic poles and applications

2008-08-20

arxiv.org/abs/0808.2698v1

Mathematics

Algebraic Geometry

46 pages

Scientific paper

10.1007/s00220-008-0699-7

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 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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