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

Johannes Huisman (1) , Frédéric Mangolte (2)

1 LM-Brest - Laboratoire de Mathématiques
2 LAMA - Laboratoire de Mathématiques

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.

Mots clés: uniruled algebraic variety; Seifert manifold; lens space; connected sum; equivariant line bundle; real algebraic model

Domaines: Géométrie algébrique [math.AG]

Johannes Huisman, Frédéric Mangolte. Every connected sum of lens spaces is a real component of a uniruled algebraic variety. Annales de l'Institut Fourier, 2005, 55, pp.2475-2487. ⟨hal-00003485v2⟩