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A construction theorem for Frobenius manifolds with logarithmic poles isestablished. This is a generalization of a theorem of Hertling and Manin. As anapplication we prove a generalization of the reconstruction theorem ofKontsevich and Manin for projective smooth varieties with convergentGromov-Witten potential. A second application is a construction of Frobeniusmanifolds out of a variation of polarized Hodge structures which degeneratesalong a normal crossing divisor when certain generation conditions arefulfilled.

A construction of Frobenius manifolds with logarithmic poles and applications