Every connected sum of lens spaces is a real component of a uniruled algebraic variety

Abstract : Let M be a connected sum of finitely many lens spaces, and let N be a connected sum of finitely many copies of S^1xS^2. We show that there is a uniruled algebraic variety X such that the connected sum M#N of M and N is diffeomorphic to a connected component of the set of real points X(R) of X. In particular, any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled algebraic variety.
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Submitted on : Friday, March 18, 2005 - 6:24:54 PM
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Johannes Huisman, Frédéric Mangolte. Every connected sum of lens spaces is a real component of a uniruled algebraic variety. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2005, 55, pp.2475-2487. ⟨hal-00003485v2⟩

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