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Rational singularities and quotients by holomorphic group actions

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.

preprint2010arXivOpen access
Daniel Greb
math.CVmath.AG
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Daniel Greb

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