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PreprintCC BY-NC-SA 4.0arXiv

Exceptional Loci and Hyperbolicity of Complements of Plane Curves with c̅12 − c̅2 > 0

  • Wei Chen
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Abstract

Let B be a plane curve which has simple normal crossings. We prove that, if B = B_1 \cup B_2 has two irreducible components with deg B_1, deg B_2 \geq 5 or deg B_1 = 4, deg B_2 \geq 7, and if B is general, then the associated algebraic exceptional set is empty. Based on this, we show that for a general plane curve B satisfying \bar{c}_1^2 - \bar{c}_2 > 0, the open surface \mathbb{P}^2 \setminus B is Kobayashi hyperbolic.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026exceptional,
  title = {{Exceptional Loci and Hyperbolicity of Complements of Plane Curves with $\barc_1^2 - \barc_2 > 0$}},
  author = {Wei Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37777},
  eprint = {2609.37777},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37777},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Exceptional Loci and Hyperbolicity of Complements of Plane Curves with c̅_1^2 − c̅_2 > 0
AU  - Wei Chen
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37777
UR  - https://arxiv.org/abs/2609.37777
AB  - Let B be a plane curve which has simple normal crossings. We prove that, if B = B_1 \cup B_2 has two irreducible components with deg B_1, deg B_2 \geq 5 or deg B_1 = 4, deg B_2 \geq 7, and if B is general, then the associated algebraic exceptional set is empty. Based on this, we show that for a general plane curve B satisfying \bar{c}_1^2 - \bar{c}_2 > 0, the open surface \mathbb{P}^2 \setminus B is Kobayashi hyperbolic.
ER  -