6533b7cffe1ef96bd12597ad
RESEARCH PRODUCT
Frobenius polynomials for Calabi–Yau equations
Kira SamolDuco Van Stratensubject
Pure mathematicsPolynomialAlgebra and Number TheoryModular formHolomorphic functionGeneral Physics and AstronomyUnipotentMathematics::Algebraic GeometryQuadratic equationMonodromyCalabi–Yau manifoldFourier seriesMathematical PhysicsMathematicsdescription
We describe a variation of Dwork’ s unit-root method to determine the degree 4 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 [3]. For singular points, we find that the Frobenius polynomial splits in a product of two linear factors and a quadratic part 1− apT + p3T 2. We identify weight 4 modular forms which reproduce the ap as Fourier coefficients.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 | Communications in Number Theory and Physics |