Saved in:
Bibliographic Details
Main Author: Zhang, Shiyu
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.17237
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916059846541312
author Zhang, Shiyu
author_facet Zhang, Shiyu
contents We record two remarks. First, for a compact Kähler manifold with semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration is exactly the number of non-truly-flat directions. Second, for compact Kähler manifolds with quasi-negative $k$-Ricci curvature, $1<k<n$, or more generally with quasi-negative mixed curvature $C_{a,b}$ for $a,b>0$, the canonical bundle is ample.
format Preprint
id arxiv_https___arxiv_org_abs_2508_17237
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Remark on semi-positive holomorphic sectional curvature and quasi-negative $k$-Ricci curvature
Zhang, Shiyu
Differential Geometry
We record two remarks. First, for a compact Kähler manifold with semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration is exactly the number of non-truly-flat directions. Second, for compact Kähler manifolds with quasi-negative $k$-Ricci curvature, $1<k<n$, or more generally with quasi-negative mixed curvature $C_{a,b}$ for $a,b>0$, the canonical bundle is ample.
title Remark on semi-positive holomorphic sectional curvature and quasi-negative $k$-Ricci curvature
topic Differential Geometry
url https://arxiv.org/abs/2508.17237