Abstract.
For a variety where a connected linear algebraic group acts with only finitely many orbits, each of which admits an attractive slice, we show that the stratification by orbits is perfect for equivariant intersection cohomology with respect to any equivariant local system. This applies to provide a relationship between the vanishing of the odd dimensional intersection cohomology sheaves and of the odd dimensional global intersection cohomology groups. For example, we show that odd dimensional intersection cohomology sheaves and global intersection cohomology groups vanish for all complex spherical varieties.
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Received: 25 February 2000 / Accepted: 15 February 2001 / Published online: 23 July 2001
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Brion, M., Joshua, R. Vanishing of odd dimensional intersection cohomology II. Math Ann 321, 399–437 (2001). https://doi.org/10.1007/s002080100235
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DOI: https://doi.org/10.1007/s002080100235