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Degeneration of the Leray spectral sequence for certain geometric quotients. (English) Zbl 1049.14035
Summary: We prove that the Leray spectral sequence in rational cohomology for the quotient map $$U_{n,d}\to U_{n,d}/G$$ where $$U_{n,d}$$ is the affine variety of equations for smooth hypersurfaces of degree $$d$$ in $$\mathbb P^n(\mathbb C)$$ and $$G$$ is the general linear group, degenerates at $$E_2$$.

##### MSC:
 14L30 Group actions on varieties or schemes (quotients) 14J70 Hypersurfaces and algebraic geometry 14D20 Algebraic moduli problems, moduli of vector bundles 14F99 (Co)homology theory in algebraic geometry 55T99 Spectral sequences in algebraic topology
##### Keywords:
geometric quotient; hypersurfaces; Leray spectral sequence
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