Rational singularities and quotients by holomorphic group actions
arXiv:0906.4623 · doi:10.2422/2036-2145.2011.2.07
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 Boutot 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.
13 pages; typos corrected, references added and updated; to appear in Annali della Scuola Normale Superiore, Classe di Scienze.