Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2608.09114

Nef but Non-Semi-positive Line Bundles on Hopf Manifolds

Xiaojun Wu
View original source ↗Read source document ↗Export metadata ↓

Abstract

We give a complete characterization of the nef, effective, pseudo-effective, and semi-positive cones on Hopf manifolds. In particular, by computing the Ueda classes on non-diagonal Hopf surfaces, we show that the invariant elliptic curve is nef but not semi-positive. Via Bott--Chern cohomology calculations, we construct new examples of nef but non-semi-positive line bundles on Hopf manifolds of arbitrary dimension.

Explore related subjects

math.CVmath.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xiaojun Wu. 2026-08-10. Nef but Non-Semi-positive Line Bundles on Hopf Manifolds. https://arxiv.org/abs/2608.09114

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Uniform RC-positivity of tangent bundles

In this paper, we prove that every rationally connected projective manifold admits a smooth uniformly RC-positive Hermitian metric on its tangent bundle, answering Yang's question and giving a characterization of rational connectedness by uniform RC-positivity. We find an example to show that RC-positivity alone does not characterize rational connectedness. We also prove that uniform RC-positivity of the tangent bundle is preserved under blow-ups along connected smooth centers on compact complex manifolds. In the non-Kähler setting, we construct such metrics on all Hopf and Kato surfaces and obtain classification results for compact complex surfaces.

math.CV↗
arXiv2026

Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions

In this paper, we investigate the growth, distortion, pre-Schwarzian and Schwarzian norms of functions in the exponentially convex class \(\mathcal C_{e^λ}\), \(0<λ\leπ/2\), defined by \(1+zf''(z)/f'(z)\prec e^{λz}\). By representing the associated Schwarz function explicitly, we derive parameter-dependent estimates for \(f\), \(f'\), and the pre-Schwarzian derivative. We further obtain Schwarzian norm estimates under both the general normalization and the additional condition \(f''(0)=0\). The corresponding extremal problems are analyzed through suitable Schwarz functions, and the dependence of the resulting bounds on the exponential parameter is made explicit.

math.CV↗