8 papers
Oka complements in algebraic tori and their logarithmic covers
Yun-Heng Du, Bin Guo, Peng-Chao Wang +1
Suppose and $K\subset\C^n$ is compact and polynomially convex. Write , $X_K=(\C^*)^n\setminus(K\cap(\C^*)^n)$, and $Y_K=\C^n\setminus q^{…
Oka Geometry of Complex Six-Spheres
Yun-Heng Du, Bin Guo, Yuta Kusakabe +1
Alpöge constructed a complex structure on through a torus fibration with exactly three special fibres. We prove that every member of the associated admissible period family i…
A first-jet characterization of Griffiths positivity
Yun-Heng Du, Song-Yan Xie
We characterize Griffiths positivity of vector bundles on smooth projective varieties by a finite-dimensional convex condition on first jets of sections of positive twists. A nonze…
Ample vector bundles without Griffiths-semipositive metrics
Yun-Heng Du, Song-Yan Xie
We construct a rank-two ample holomorphic vector bundle on an abelian surface that admits no smooth Griffiths-semipositive Hermitian metric, thereby giving a counterexample to the…
Analytic and Algebraic Oka-1 Approximation for Smooth Projective Morphisms with Rationally Connected Fibers
Yun-Heng Du, Bin Guo, Song-Yan Xie
Let be a smooth projective morphism of complex manifolds with connected rationally connected fibers. We prove holomorphic approximation on arbitrary compact sets…
Analytic Construction of Rational Curves on Fano Manifolds
Yun-Heng Du, Bin Guo, Song-Yan Xie
Inspired by constructions of entire curves in Oka geometry, we construct rational curves on complex Fano manifolds analytically, by alternately deforming a holomorphic disk to redu…
Some Examples and Counterexamples in Oka Theory
Yun-Heng Du
This paper gives examples and counterexamples in Oka theory: two about deleting closed sets from complex Euclidean space, one about blowing up along a connected Oka center, and one…
Sharp Summability of Nevanlinna Defects for Finite-Lower-Order Holomorphic Curves
Yun-Heng Du, Song-Yan Xie
For a countable family of hyperplanes , , in general position and a linearly nondegenerate holomorphic curve $f\colon \mathbb{C}\to \mathbb…