Rational singularities and quotients by holomorphic group actions
Complex Variables
2015-04-17 v2 Algebraic Geometry
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.
Cite
@article{arxiv.0906.4623,
title = {Rational singularities and quotients by holomorphic group actions},
author = {Daniel Greb},
journal= {arXiv preprint arXiv:0906.4623},
year = {2015}
}
Comments
13 pages; typos corrected, references added and updated; to appear in Annali della Scuola Normale Superiore, Classe di Scienze.