Degeneration of the Leray spectral sequence for certain geometric quotients. (English) Zbl 1049.14035

Peters, C. A. M.; Steenbrink, J. H. M.

Mosc. Math. J. 3, No. 3, 1085-1095 (2003).

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