In this paper we establish the action of the Grothendieck-Teichmüller group on the prime order torsion elements of the profinite fundamental group . As an intermediate result, we prove that the conjugacy classes of prime order torsion of are exactly the discrete prime order ones of the .
We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem...
We consider a nondegenerate holomorphic map where is a compact Hermitian manifold of dimension larger than or equal to and is an open connected complex manifold of dimension . In this article we give criteria which permit to construct Ahlfors’ currents in .