Degeneration of the Leray Spectral Sequence for Certain Geometric Quotients
نویسندگان
چکیده
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 P(C) and G is the general linear group, degenerates at E2. 2000 Math. Subj. Class. 14D20, 14L35, 14J70.
منابع مشابه
2 00 1 Degeneration of the Leray spectral sequence for certain geometric quotients
We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .
متن کامل2 5 Ja n 20 02 Degeneration of the Leray spectral sequence for certain geometric quotients
We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .
متن کاملFibered Symplectic Cohomology and the Leray-serre Spectral Sequence
We define Symplectic cohomology groups FH∗ [a,b] (E), −∞ ≤ a < b ≤ ∞ for a class of symplectic fibrations F →֒ E −→ B with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. When B is symplectically aspherical we construct a spectral sequence of Leray-Serre ty...
متن کاملFibered Symplectic Homology and the Leray-serre Spectral Sequence
We define Floer (or Symplectic) cohomology groups FH ]a, b] (E), −∞ ≤ a < b ≤ ∞ for a class of monotone symplectic fibrations F →֒ E −→ B with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. Our construction is a fibered extension of a construction of Viter...
متن کاملAdiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
We first prove an adiabatic limit formula for the rf-invariant of aDirac operator, generalizing the recent work of J.-M. Bismut and J. Cheeger.An essential part of the proof is the study of the spectrum of the Dirac op-erator in the adiabatic limit. A new contribution arises in the adiabatic limitformula, in the form of a global term coming from the (asymptotically) verysmal...
متن کامل