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Nef but Non-Semi-positive Line Bundles on Hopf Manifolds
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. We also prove that a minimal compact complex surface X containing an elliptic curve C and a nef line bundle L such that (X,C,L) has finite generalized Ueda type is either a Hopf surface or Serre's example.
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BibTeX
@misc{wu2026nonsemipositive,
title = {{Nef but Non-Semi-positive Line Bundles on Hopf Manifolds}},
author = {Xiaojun Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.09114},
eprint = {2608.09114},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.09114},
}
RIS
TY - UNPB
TI - Nef but Non-Semi-positive Line Bundles on Hopf Manifolds
AU - Xiaojun Wu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2608.09114
UR - https://arxiv.org/abs/2608.09114
AB - 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. We also prove that a minimal compact complex surface X containing an elliptic curve C and a nef line bundle L such that (X,C,L) has finite generalized Ueda type is either a Hopf surface or Serre's example.
ER -