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

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

2004-12-08

arxiv.org/abs/math/0412159v2

Annales de l'Institut Fourier 55 (2005) 2475-2487

Mathematics

Algebraic Geometry

Nouvelle version avec deux figures

Scientific paper

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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