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Frobenius polynomials for Calabi-Yau equations

Kira Samol, Duco van Straten

Number 5
Authors Kira Samol
Duco van Straten
Project A13
Year 2008

We describe a variation of Dworks unit-root method to determine the degree four Frobenius polynomial for members of a 1-modulus Calabi-Yau family over P1 in terms of the holomorphic period near a point of maximal unipotent monodromy. The method is illustrated on a couple of examples from the list [2]. For singular points we find that the Frobenius polynomial splits, as expected, in a product of two linear factors and a quadratic part 1+apT+p3T3. We identify weight four modular forms which reproduce the ap as Fourier coefficients.

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