Configuration spaces of tori
Abstract
The configuration space Cn of unordered n-tuples of distinct points on a torus T2 is a non-singular complex algebraic variety. We study holomorphic self-maps of Cn and prove that for n>4 any such map F either carries the whole of Cn into an orbit of the diagonal Aut(T2) action in Cn or is of the form F(x)=T(x)x for some holomorphic map T:Cn-->Aut(T2). We also prove that for n>4 any endomorphism of the torus braid group Bn(T2) with a non-abelian image preserves the pure torus braid group PBn(T2).
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