Greb, Daniel Rational singularities and quotients by holomorphic group actions. (English) Zbl 1241.32017 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 10, No. 2, 413-426 (2011). Author’s abstract: We prove that rational and 1-rational singularities of complex spaces are stable under taking quotients by holomorphic actions of reductive and compact Lie groups. This extends a result of J.-F. Boutot [Invent. Math. 88, 65–68 (1987; Zbl 0619.14029)] to the analytic category and yields a refinement of his result in the algebraic category. As one of the main technical tools vanishing theorems for cohomology groups with support on fibres of resolutions are proven. Reviewer: Alexandre Fernandes (Fortaleza) Cited in 1 Document MSC: 32M05 Complex Lie groups, group actions on complex spaces 32S05 Local complex singularities 32C36 Local cohomology of analytic spaces 14L30 Group actions on varieties or schemes (quotients) Keywords:rational singularities; holomorphic group actions Citations:Zbl 0619.14029 PDFBibTeX XMLCite \textit{D. Greb}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 10, No. 2, 413--426 (2011; Zbl 1241.32017) Full Text: DOI arXiv