Quasirationale Singularitäten. (Quasirational singularities) (Q1076745)

It is shown that Elkik's results [\textit{R. Elkik}, Invent. Math. 47, 139- 147 (1978; Zbl 0363.14002)] on deformations of rational singularities hold without Cohen-Macaulay assumptions: Let \(f:\quad X\to S\) be flat with normal fibres \(X_ s\) and desingularisations \(\delta_ s:\quad Y_ s\to X_ s;\) then the sets \(\{x\in X:\quad R^ i\delta_{f(x)^*}{\mathcal O}_{Y_{f(x)}}=0\quad for\quad i\geq d\}\) are open for all d.