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Preprints

• 1. Hole probabilities of random zeros on compact Riemann surfaces
  Hao Wu, Song-Yan Xie
  arXiv:2406.19114 📄 PDF
  math.CV | math.AG | math.PR
• 2. Generating all Ahlfors currents by a single entire curve
  Yunling Chen, John Erik Fornæss, Song-Yan Xie
  arXiv:2511.12473 📄 PDF
  math.CV
• 3. A Second Main Theorem for Entire Curves Intersecting Three Conics
  Lei Hou, Dinh Tuan Huynh, Joël Merker, Song-Yan Xie
  arXiv:2512.03948 📄 PDF 📦 C++ Evidence 📦 Maple Evidence
  math.CV | math.AG
• 4. Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two
  Lei Hou, Dinh Tuan Huynh, Joël Merker, Song-Yan Xie
  arXiv:2603.14881 📄 PDF 📦 Maple Evidence
  math.CV | math.AG
• 5. A Symmetry Method for Key Vanishing Lemmas and the 2-Jet Riemann--Roch Thresholds
  Tao Cui, Lei Hou, Jianjun Liu, Song-Yan Xie
  arXiv:2606.19155 📄 PDF
  math.CV | math.AG
• 6. Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection
  Pengchao Wang, Song-Yan Xie
  arXiv:2607.11021 📄 PDF
  math.CV
• 7. Elliptic complements of cubic hypersurfaces
  Song-Yan Xie
  arXiv:2608.02413 📄 PDF
  math.AG | math.CV
• 8. Sharp Summability of Nevanlinna Defects for Finite-Lower-Order Holomorphic Curves
  Yun-Heng Du, Song-Yan Xie
  arXiv:2608.20216 📄 PDF
  math.CV
• 9. Invariant two-jets and effective hyperbolicity for complements of two plane curves
  Lei Hou, Pengchao Wang, Song-Yan Xie
  arXiv:2608.22714 📄 PDF 📦 C++ Evidence
  math.CV | math.AG
• 10. Periods of Oka K3 surfaces are dense
  Song-Yan Xie, Shengyuan Zhao
  arXiv:2608.24392 PDF
  math.CV | math.AG
• 11. Kobayashi Hyperbolicity of General Surfaces via the Poincaré Problem
  Song-Yan Xie, Shengyuan Zhao
  arXiv:2609.06644 PDF
  math.AG | math.CV
• 12. Analytic Construction of Rational Curves on Fano Manifolds
  Yun-Heng Du, Bin Guo, Song-Yan Xie
  arXiv:2609.11612Short PDFEffective PDFarXiv Long PDF
  math.CV | math.AG
• 13. Analytic and Algebraic Oka-1 Approximation for Smooth Projective Morphisms with Rationally Connected Fibers
  Yun-Heng Du, Bin Guo, Song-Yan Xie
  arXiv:2609.11883PDF
  math.CV | math.AG

Publications

• 1. On the ampleness of the cotangent bundles of complete intersections
  Song-Yan Xie
  Invent. Math. 212 (2018), no. 3, 941–996.
  📄 PDF
• 2. Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree
  Dinh Tuan Huynh, Duc-Viet Vu, Song-Yan Xie
  Ann. Inst. Fourier (Grenoble) 69 (2019), no. 2, 653–671.
  📄 PDF
• 3. On Ahlfors currents
  Dinh Tuan Huynh, Song-Yan Xie
  J. Math. Pures Appl. (9) 156 (2021), 307–327.
  📄 PDF
• 4. On the Weyl-Ahlfors theory of derived curves
  Dinh Tuan Huynh, Song-Yan Xie
  Math. Z. 300 (2022), no. 1, 475–491.
  📄 PDF
• 5. Universal entire curves in projective spaces with slow growth
  Zhangchi Chen, Dinh Tuan Huynh, Song-Yan Xie
  J. Geom. Anal. 33 (2023), no. 9, Paper No. 308, 12 pp.
  📄 PDF
• 6. Big Picard theorem for jet differentials and non-archimedean Ax-Lindemann theorem
  Dinh Tuan Huynh, Ruiran Sun, Song-Yan Xie
  J. Number Theory 253 (2023), 257–277.
  📄 PDF
• 7. Universal holomorphic maps with slow growth I: an algorithm
  Bin Guo, Song-Yan Xie
  Math. Ann. 389 (2024), 3349–3378.
  📄 PDF
• 8. Entire curves producing distinct nevanlinna currents
  Song-Yan Xie
  Int. Math. Res. Not. 2024 (2024), no. 10, 8350–8362.
  📄 PDF
• 9. Universal holomorphic maps with slow growth II: functional analysis methods
  Bin Guo, Song-Yan Xie
  Indiana Univ. Math. J. 75 (2026), no. 1, 48–86.
  📄 PDF
• 10. Entire holomorphic curves into Pn(C) intersecting n+1 general hypersurfaces
  Zhangchi Chen, Dinh Tuan Huynh, Ruiran Sun, Song-Yan Xie
  Sci. China Math. 68 (2025), no. 12, 2847–2866.
  📄 PDF
• 11. Entire curves generating all shapes of Nevanlinna currents
  Hao Wu, Song-Yan Xie
  J. Lond. Math. Soc. (2) 111 (2025), no. 5, Paper No. e70177.
  📄 PDF
• 12. Frequently hypercyclic meromorphic curves with slow growth
  Zhangchi Chen, Bin Guo, Song-Yan Xie
  J. Geom. Anal. 36 (2026), 132.
  📄 PDF