2022/09/29 by Li, Ping · 1 citation
#32L20 #32Q10 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2209.14554
A vanishing theorem for uniformly RC k-positive Hermitian holomorphic vector bundles is established. It turns out that the holomorphic tangent bundle of a compact complex manifold equipped with a positive k-Ricci curvature Kähler metric is uniformly RC k-positive. Two main applications are presented. The first one is to deduce that spaces of some holomorphic tensor fields on such Kähler or more generally Kähler-like Hermitian manifolds are trivial, generalizing some recent results. The second one is to show that a compact Kähler manifold whose holomorphic tangent bundle can be endowed with either a uniformly RC k-positive Hermitian metric or a positive k-Ricci curvature Kähler-like Hermitian metric is projective and rationally connected.