K\"ahler manifolds of semi-negative holomorphic sectional curvature
By Gordon Heier, Steven Lu, B. Wong. 2014
51 citations recorded by the source corpus.
In an earlier work, we investigated some consequences of the existence of a K\"ahler metric of negative holomorphic sectional curvature on a projective manifold. In the present work, we extend our results to the case of semi-negative (i.e., non-positive) holomorphic sectional curvature. In doing so, we define a new invariant that records the largest codimension of maximal subspaces in the tangent spaces on which the holomorphic sectional curvature vanishes. Using this invariant, we establish lower bounds for the nef dimension and, under certain additional assumptions, for the Kodaira dimension of the manifold. In dimension two, a precise structure theorem is obtained.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1e6248e72afe01ec148a60a06173c6220e236f28
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- RC-positivity, rational connectedness and Yau's conjecture (2017, background): “fold. In [47], Wu and Yau give a direct proof of the statement that any compact Ka¨hler manifold with quasi-negative holomorphic sectional curvature must have ample canonical line bundle. We refer to [43, 25, 44, 26, 46, 47, 41, 20, 54, 42] for more details. On the other hand, it is wellknown that t”
- Negative holomorphic curvature and positive canonical bundle (2015, unknown): “itional assumption that the Picard number of the projective manifold is equal to 1. Our method is essentially the refined Schwarz type lemma. Recently, some important progress is made by Heier-Lu-Wong [5, 6], which combines the algebraic-geometric method and the analytic method. Along with other inte”