Rational singularities and quotients by holomorphic group actions

Details Rational singularities and quotients by holomorphic group actions Rational singularities and quotients by holomorphic group actions

2009-06-25

arxiv.org/abs/0906.4623v2

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. X, issue 2 (2011), 413-426

Mathematics

Complex Variables

13 pages; typos corrected, references added and updated; to appear in Annali della Scuola Normale Superiore, Classe di Scienze

Scientific paper

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.

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