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Zbl 1092.14070
Huisman, Johannes; Mangolte, Frédéric
Every connected sum of lens spaces is a real component of a uniruled algebraic variety. (English)
[J] Ann. Inst. Fourier 55, No. 7, 2475-2487 (2005). ISSN 0373-0956; ISSN 1777-5310/e

The main result of the paper is that a connected sum of lens spaces is always diffeomorphic to a connected component of a real algebraic uniruled $3$-manifold. This answers in the affirmative a conjecture by {\it J. Kollár} [in: Taniguchi conference on mathematics Nara '98. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 31, 127--145 (2001; Zbl 1036.14010)]. The proof is close to that from an earlier paper of the authors [Topology 44, No. 1, 63--71 (2005; Zbl 1108.14048)], where every orientable Seifert $3$-manifold is shown to be diffeomorphic to a component of a real algebraic uniruled $3$-manifold; its main idea is to represent a connected sum of lens spaces as a Werther fibration over a smooth surface with boundary.
[Eugenii I. Shustin (Tel Aviv)]

MSC 2000:: *14P25 Topology of real algebraic varieties
57M50 Geometric structures on low-dimensional manifolds
57N10 Topology of general 3-manifolds

Keywords: Seifert fibred manifold; lens space; equivariant line bundle; real algebraic

Citations: Zbl 1036.14010; Zbl 1108.14048

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