Song-Yan Xie

activity

20152026

most citedOn the ampleness of the cotangent bundles of complete intersections

7 citations · 25 across the 22 of their papers we have counts for

collaborators

31 papers

math.CV2026

Oka complements in algebraic tori and their logarithmic covers

Yun-Heng Du, Bin Guo, Peng-Chao Wang +1

Suppose $n \geq 2$ and $K\subset\C^n$ is compact and polynomially convex. Write $q (z) = (e^{- i z_{1}}, \dots, e^{- i z_{n}})$ , $X_K=(\C^*)^n\setminus(K\cap(\C^*)^n)$, and $Y_K=\C^n\setminus q^{…

math.CV2026

Exponential Green energies, quantization, and minimizers on compact Riemann surfaces

Haakan Hedenmalm, Song-Yan Xie

We study the exponential Green energies associated with a finite point configuration on a Riemann surface. We focus on studying optimal or close-to-optimal configurations, and show…

cs.LG2026

Mixing Regularization for Average-Reward $Q$ -Learning and $Q$ -Planning

Julien Roger, Sam Bodmer, Jian Qian +1

The average-reward setting for reinforcement learning is challenging because its Bellman operator is known to contract in span only when the underlying Markov chain is mixing. Wher…

math.CV2026

Oka manifolds are ubiquitous

Sicheng An, Bin Guo, Yun-Heng Du +2

We prove that a holomorphic family of connected complex Lie groups has Oka total space if and only if its base is Oka. Extension presentations and generating sections give Oka resu…

cs.IT2026

Network Coding Can Beat Routing in Undirected Multiple-Unicast Networks

Xindan Zhang, Baochun Li, Zongpeng Li

Network coding lets the nodes of a network combine messages rather than merely forward them. In undirected networks, where the two directions of an edge share its capacity, Li and…

math.CV2026

Oka Geometry of Complex Six-Spheres

Yun-Heng Du, Bin Guo, Yuta Kusakabe +1

Alpöge constructed a complex structure on $S^{6}$ through a torus fibration with exactly three special fibres. We prove that every member of the associated admissible period family i…

math.CV2026

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…

math.CV2026

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…

math.CV2026

Analytic and Algebraic Oka-1 Approximation for Smooth Projective Morphisms with Rationally Connected Fibers

Yun-Heng Du, Bin Guo, Song-Yan Xie

Let $π : Z \to Y$ be a smooth projective morphism of complex manifolds with connected rationally connected fibers. We prove holomorphic approximation on arbitrary compact sets…

math.CV2026

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…

math.AG2026

Kobayashi Hyperbolicity of General Surfaces via the Poincaré Problem

Song-Yan Xie, Shengyuan Zhao

We prove that a general surface in $P^{3}$ of degree at least $18$ contains no rational or elliptic curves, strengthening the classical result of Clemens by replacing the or…

math.AG2026

Invariant two-jets and effective hyperbolicity for complements of two plane curves

Lei Hou, Pengchao Wang, Song-Yan Xie

Let $D = C_{1} + C_{2} \subset P^{2}$ be a simple-normal-crossing union of smooth plane curves of degrees $1 ⩽ d_{1} ⩽ d_{2}$ . We prove an effective Second Main Theorem on a…

math.CV2026

Periods of Oka K3 surfaces are dense

Song-Yan Xie, Shengyuan Zhao

We give the first known examples of Oka Calabi--Yau manifolds in any dimension: every smooth hypersurface of multidegree $(2, \dots, 2)$ in a product of projective lines is Oka. Bui…

math.CV2026

Sharp Summability of Nevanlinna Defects for Finite-Lower-Order Holomorphic Curves

Yun-Heng Du, Song-Yan Xie

For a countable family of hyperplanes $H_{j} \subset P^{m}$ , $j \in N$ , in general position and a linearly nondegenerate holomorphic curve $f\colon \mathbb{C}\to \mathbb…

math.AG2026

Elliptic complements of cubic hypersurfaces

Song-Yan Xie

Let $D \subset P^{n}$ , $n ⩾ 2$ , be an arbitrary cubic hypersurface, and let $D_{red}$ denote its reduced support. We prove that $P^{n} ∖ D$ is hol…

math.CV2026

Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection

Pengchao Wang, Songyan Xie

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…

math.AG2026

A Symmetry Method for Key Vanishing Lemmas and Optimal $2$ -Jet Thresholds for Hyperbolicity

Tao Cui, Lei Hou, Jianjun Liu +1

This manuscript reports on an ongoing project. The finite full-column-rank computations underlying the Key Vanishing Lemmas isolated below are currently undergoing exact computer-a…

math.CV2026

Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two

Lei Hou, Dinh Tuan Huynh, Joël Merker +1

This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in $P^{3}$ of degree at least $17$ is…

math.CV2025

A Second Main Theorem for Entire Curves Intersecting Three Conics

Lei Hou, Dinh Tuan Huynh, Joël Merker +1

We establish a Second Main Theorem for algebraically nondegenerate entire holomorphic curves $ f: \mathbb{C} \to \mathbb{P}^2 $ intersecting a generic configuration of three coni…

math.CV2023

Entire holomorphic curves into $P^{n} (C)$ intersecting $n + 1$ general hypersurfaces

Zhangchi Chen, Dinh Tuan Huynh, Ruiran Sun +1

Let ${D_{i}}_{i = 1}^{n + 1}$ be $n + 1$ hypersurfaces in $P^{n} (C)$ with total degrees $\sum_{i = 1}^{n + 1} ° D_{i} ⩾ n + 2$ , in general position and satisfying a generic…

math.CV2023

Entire curves generating all shapes of Nevanlinna currents

Hao Wu, Song-Yan Xie

First, we show that every complex torus $T$ contains some entire curve $g : C \to T$ such that the concentric holomorphic discs $\{g\restriction_{\…

math.CV2023★ 2 cited

Entire curves producing distinct Nevanlinna currents

Song-Yan Xie

First, inspired by a question of Sibony, we show that in every compact complex manifold $Y$ with certain Oka property, there exists some entire curve $f : C \to Y$ g…

math.CV2023★ 3 cited

Universal holomorphic maps with slow growth I. An Algorithm

Bin Guo, Song-Yan Xie

We design an Algorithm to fabricate universal holomorphic maps between any two complex Euclidean spaces, within preassigned transcendental growth rate. As by-products, universal ho…

math.CV2023★ 3 cited

Universal Entire Curves in Projective Spaces with Slow Growth

Zhangchi Chen, Dinh Tuan Huynh, Song-Yan Xie

We construct explicit universal entire curves in projective spaces whose Nevanlinna characteristic functions grow slower than any preassigned transcendental growth rate. Moreover,…

Oka complements in algebraic tori and their logarithmic covers

Exponential Green energies, quantization, and minimizers on compact Riemann surfaces

Mixing Regularization for Average-Reward Q-Learning and Q-Planning

Oka manifolds are ubiquitous

Network Coding Can Beat Routing in Undirected Multiple-Unicast Networks

Oka Geometry of Complex Six-Spheres

A first-jet characterization of Griffiths positivity

Ample vector bundles without Griffiths-semipositive metrics

Analytic and Algebraic Oka-1 Approximation for Smooth Projective Morphisms with Rationally Connected Fibers

Analytic Construction of Rational Curves on Fano Manifolds

Kobayashi Hyperbolicity of General Surfaces via the Poincaré Problem

Invariant two-jets and effective hyperbolicity for complements of two plane curves

Periods of Oka K3 surfaces are dense

Sharp Summability of Nevanlinna Defects for Finite-Lower-Order Holomorphic Curves

Elliptic complements of cubic hypersurfaces

Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection

A Symmetry Method for Key Vanishing Lemmas and Optimal 2-Jet Thresholds for Hyperbolicity

Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two

A Second Main Theorem for Entire Curves Intersecting Three Conics

Entire holomorphic curves into Pn(C) intersecting n+1 general hypersurfaces

Entire curves generating all shapes of Nevanlinna currents

Entire curves producing distinct Nevanlinna currents

Universal holomorphic maps with slow growth I. An Algorithm

Universal Entire Curves in Projective Spaces with Slow Growth

Mixing Regularization for Average-Reward $Q$ -Learning and $Q$ -Planning

A Symmetry Method for Key Vanishing Lemmas and Optimal $2$ -Jet Thresholds for Hyperbolicity

Entire holomorphic curves into $P^{n} (C)$ intersecting $n + 1$ general hypersurfaces