PreprintarXiv licencearXiv
Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection
Abstract
Noguchi introduced the notion of Wronskian curvature positivity in his Second Main Theorem and asked for further examples to which his theorem applies. We give a complete answer: a complex manifold admits a smooth connection satisfying this condition if and only if it admits a holomorphic projective connection. For a fixed torsion-free connection, the condition is equivalent to the holomorphicity of its projective class.
Related
- A numerically flat rank-two bundle without a holomorphic connection on a ∂∂̅-threefold
- Gauss-Manin Connection in Disguise: Holomorphic Anomaly Equations and Higher Genus Real Gromov-Witten Invariants
- Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
- Meromorphic approximation of holomorphic maps into algebraically elliptic projective varieties
- Holomorphic functions on complete Hermitian manifolds with flat Chern connection, II
BibTeX
@misc{wang2026wronskian,
title = {{Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection}},
author = {Pengchao Wang and Songyan Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.11021},
eprint = {2607.11021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11021},
}
RIS
TY - UNPB
TI - Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection
AU - Pengchao Wang
AU - Songyan Xie
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2607.11021
UR - https://arxiv.org/abs/2607.11021
AB - Noguchi introduced the notion of Wronskian curvature positivity in his Second Main Theorem and asked for further examples to which his theorem applies. We give a complete answer: a complex manifold admits a smooth connection satisfying this condition if and only if it admits a holomorphic projective connection. For a fixed torsion-free connection, the condition is equivalent to the holomorphicity of its projective class.
ER -