Real algebraic principal abelian fibrations

If M is a closed smooth manifold, it is well known that M is diffeomorphic to a nonsingular real algebraic set. Let G be a finite group and let X→πY be a principal G-fibration where X and Y are closed smooth manifolds. By the first sentence, we can assume Y is a nonsingular real algebraic set. Question: Is X→πY differentiably equivalent to an algebraic principal G-fibration X~→π~Y (X~, π~ and the action of G on X~ all algebraic)? The author defines an "algebraic cohomology group'' H1A(Y,G) in the case G=(Z/2)k×H, where H is an abelian group of odd order. It is a subgroup of H1(Y,G) and generalizes the usual notion of algebraic cohomology when G=Z/2. The above question is then answered as follows: The existence of X~→π~Y is equivalent to the existence of a regular (= algebraic) classifying map ϕ:Y→K(G,1). Here K(G,1) is an Eilenberg-Mac Lane space which can be realized as the limit of algebraic sets (this uses the special assumption on the type of G) so that algebraicity of the classifying map makes sense. A typical application of the above is the construction of compact nonsingular algebraic sets which admit no nontrivial algebraic G-fibrations.
Contemporary Math


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It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their de. ning ideals in the non-complete intersection case. In order to obtain this result, we determine the generators of their tangent cones explicitly by using standard b...
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Wolff, MPH; Emel'yanov, Eduard Yu. (2001-01-01)
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Effective Mass Quantum Systems with Displacement Operator: Inverse Square Plus Coulomb-Like Potential
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The Schrodinger-like equation written in terms of the displacement operator is solved analytically for a inverse square plus Coulomb-like potential. Starting from the new Hamiltonian, the effects of the spatially dependent mass on the bound states and normalized wave functions of the "usual" inverse square plus Coulomb interaction are discussed.
Citation Formats
Y. Ozan, “Real algebraic principal abelian fibrations,” Contemporary Math, 1995, Accessed: 00, 2021. [Online]. Available: