On the module of Zariski differentials and infinitesimal deformations of cusp singularities (Q1071825)

The dimension of the space of first order infinitesimal deformations of a cusp singularity (X,0) is computed in terms of its resolution graph. One basic feature of the proof is to express this dimension in terms of 1- forms on the singularity (using local duality) and to analyze such 1- forms by expanding them as Fourier series on the universal cover of X- \(\{\) \(0\}\) (which is the neighbourhood of a cusp point in the product of two copies of the upper half plane with respect to a Hilbert modular group). A different proof of the result of this paper was given by \textit{I. Nakamura} [Math. Ann., to appear].