Oberseminar SoSe 2011 Zusammenfassung des Vortrags von Swantje Gährs
A combinatorial approach to the Griffiths-Dwork method for invertible polynomials
The Griffiths-Dwork method provides an algorithm to calculate the Picard-Fuchs equation for families of hypersurfaces. I will look at the special case of a 1-parameter family f of a hypersurface given by a weighted homogeneous invertible polynomial g. Here I will explain how to translate the algorithm that calculates in the Milnor ring of f to combinatorial data. With the help of this combinatorial approach I can show that the order of the Picard-Fuchs equation is related to the weights and the degree of the transposed polynomial gt.