The decomposition theorem and the intersection cohomology of quotients in algebraic geometry
Suppose a connected reductive complex algebraic group G acts linearly on an irreducible complex projective variety X. We prove that if 1→N→G→H→1 is a short exact sequence of connected reductive groups and X ss the open set of semistable points for the action of N on X then IH H ∗(X ssN) is (non-can...
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| Published in | Journal of pure and applied algebra Vol. 182; no. 2; pp. 317 - 328 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.08.2003
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Suppose a connected reductive complex algebraic group
G acts linearly on an irreducible complex projective variety
X. We prove that if
1→N→G→H→1
is a short exact sequence of connected reductive groups and
X
ss
the open set of semistable points for the action of
N on
X then
IH
H
∗(X
ssN)
is (non-canonically) a direct summand of
IH
G
∗(X
ss)
. The inclusion is provided by the decomposition theorem and certain resolutions of the action allow us to define projections. |
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| ISSN: | 0022-4049 1873-1376 |
| DOI: | 10.1016/S0022-4049(03)00030-6 |