Resumen de Existence of cscK metrics on smooth minimal models
Given a compact Kahler manifold ¨ X it is interesting to ask whether it admits a constant scalar curvature Kahler (cscK) metric. In this short note we ¨ show that there always exist cscK metrics on compact Kahler manifolds with nef ¨ canonical bundle, thus on all smooth minimal models, and also on the blowup of any such manifold. This confirms an expectation of Jian-Shi-Song [19] and extends their main result from KX semi-ample to KX nef, with a direct proof that does not appeal to the Abundance conjecture. As a byproduct we obtain that the connected component Aut0.X / of the automorphism group of a compact Kahler manifold with ¨ KX nef is either trivial or a complex torus.
