Infinitesimal locally trivial deformation spaces of compact complex surfaces with ordinary singularities (Q1969175)

To describe locally trivial infinitesimal deformations of a surface \(S\) with ordinary singularities the author computes \(H^1(S,\Theta_S)\) (where \(\Theta_S=\text{Hom}(\Omega^1_S,{\mathcal O}_S)\)) in terms of data on the normalisation. To keep track of the cuspidal and triple points he uses the \(2\)-cubic hyperresolution of \(S\) in the sense of [\textit{F. Guillen, V. Navarro Aznar, P. Pascual-Gainza} and \textit{F. Puerta}, Lecture Notes Math. 1335 (1988; Zbl 0638.00011)].