Degeneration of the Leray spectral sequence for certain geometric quotients

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Degeneration of the Leray spectral sequence for certain geometric quotients C.A.M. Peters Department of Mathematics, University of Grenoble I UMR 5582 CNRS-UJF, 38402-Saint-Martin d'Heres France, email: J.H.M. Steenbrink? Department of Mathematics, University of Nijmegen Toernooiveld, NL-6525 ED Nijmegen The Netherlands, email: 25th March 2004 Abstract We prove that the Leray spectral sequence in rational cohomology for the quotient map Un,d ? Un,d/G where Un,d is the affine variety of equations for smooth hypersurfaces of degree d in Pn(C) and G is the general linear group, degenerates at E2. Key Words and Phrases: Geometric quotient, hypersurfaces, Leray spectral sequence Math. Subj. Class.: 14D20, 14L35, 14J70 1 Introduction We consider an affine complex algebraic group G which acts on a smooth algebraic variety X. Assume that a geometric quotient f : X ? Y for the ?The second author thanks the University of Grenoble I for its hospitality and financial support 1

  • orbifold sense

  • fundamental class

  • group

  • map a?

  • inclusion rb

  • quotient map

  • orbifold fibre

  • ductive group

  • classes ?i ?


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Degeneration of the Leray spectral sequencefor certain geometric quotientsC.A.M. PetersDepartment of Mathematics, University of Grenoble IUMR5582CNRS-UJF,38402-Saint-MartindHe`resFrance, email: peters@ujf-grenoble.frJ.H.M. SteenbrinkDepartment of Mathematics, University of NijmegenToernooiveld, NL-6525 ED NijmegenThe Netherlands, email: steenbri@sci.kun.nl25th March 2004
AbstractWe prove that the Leray spectral sequence in rational cohomologyfor the quotient mapUn,dUn,d/GwhereUn,dis the affine varietyof equations for smooth hypersurfaces of degreedinPn(C) andGisthe general linear group, degenerates atE2.Key Words and Phrases: Geometric quotient, hypersurfaces, Lerayspectral sequenceMath. Subj. Class.: 14D20, 14L35, 14J70
1 IntroductionWe consider an affine complex algebraic groupGwhich acts on a smoothalgebraic varietyX. Assume that a geometric quotientf:XYfor theThe second author thanks the University of Grenoble I for its hospitality and financialsupport
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