The -point configuration spaces and of a complex torus are complex manifolds. We prove that for any holomorphic self-map of either carries the whole of into an orbit of the diagonal action in or is of the form , where is a holomorphic map. We also prove that for any endomorphism of the torus braid group with a non-abelian image preserves the pure torus braid group .
Cite this article
Yoel Feler, Configuration spaces of tori. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 2, pp. 139–151DOI 10.4171/RLM/486