Degeneration of the Leray spectral sequence for certain geometric quotients

Peters Department

Description

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 ?

Sujets

• Department
• Fundamental class
• Quotient space
• multiplication
• maths
• Mathématiques

Informations

• Publié par: pefav
• Nombre de lectures: 11
• Langue: English

Extrait

Degeneration of the Leray spectral sequence for certain geometric quotients C.A.M. Peters Department of Mathematics, University of Grenoble I UMR5582CNRS-UJF,38402-Saint-Martind’He`res France, email: [e-mail] J.H.M. Steenbrink ∗ Department of Mathematics, University of Nijmegen Toernooiveld, NL-6525 ED Nijmegen The Netherlands, email: [e-mail] 25th March 2004

Abstract We prove that the Leray spectral sequence in rational cohomology for the quotient mapU n,d →U n,d /GwhereU n,d is the affine variety of equations for smooth hypersurfaces of degreedinP n (C) andGis the general linear group, degenerates atE 2 . Key Words and Phrases: Geometric quotient, hypersurfaces, Leray spectral sequence Math. Subj. Class.: 14D20, 14L35, 14J70

1 Introduction We consider an affine complex algebraic groupGwhich acts on a smooth algebraic varietyX. Assume that a geometric quotientf:X→Yfor the ∗ The second author thanks the University of Grenoble I for its hospitality and financial support

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