AI 中文总结
该研究刻画了Hopf流形的相关锥，证明其不变椭圆曲线为nef非半正，并借助Bott–Chern上同调在任意维Hopf流形上构造了这类线丛的新例子。
AI 中文摘要
我们完整刻画了Hopf流形上的nef、有效、伪有效及半正锥；特别地，通过计算非对角Hopf曲面上的Ueda类，证明其不变椭圆曲线是nef但非半正的；借助Bott–Chern上同调计算，我们在任意维Hopf流形上构造了新的nef但非半正的线丛例子。
英文摘要
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.
Comments33 pages; an appendix has been added in Version 2
