## A complex case of Vojta’s general abc conjecture and cases of Campana’s orbifold conjecture

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- by Ji Guo and Julie Tzu-Yueh Wang;
- Trans. Amer. Math. Soc.
**377**(2024), 4961-4991 - DOI: https://doi.org/10.1090/tran/9175
- Published electronically: April 24, 2024
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## Abstract:

We show a truncated second main theorem of level one with explicit exceptional sets for analytic maps into $\mathbb P^2$ intersecting the coordinate lines with sufficiently high multiplicities. The proof is based on a greatest common divisor theorem for an analytic map $f:\mathbb C\mapsto \mathbb P^n$ and two homogeneous polynomials in $n+1$ variables with coefficients which are meromorphic functions of the same growth as the analytic map $f$. As applications, we study some cases of Campana’s orbifold conjecture for $\mathbb P^2$ and finite ramified covers of $\mathbb P^2$ with three components admitting sufficiently large multiplicities. In addition, we explicitly determine the exceptional sets. Consequently, it implies the strong Green-Griffiths-Lang conjecture for finite ramified covers of $\mathbb G_m^2$.## References

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## Bibliographic Information

**Ji Guo**- Affiliation: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410075, China
- ORCID: 0000-0002-4374-2691
- Email: 221250@csu.edu.cn
**Julie Tzu-Yueh Wang**- Affiliation: Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan
- MR Author ID: 364623
- ORCID: 0000-0003-2133-1178
- Email: jwang@math.sinica.edu.tw
- Received by editor(s): December 19, 2022
- Received by editor(s) in revised form: November 28, 2023, and November 29, 2023
- Published electronically: April 24, 2024
- Additional Notes: The first author was supported in part by National Natural Science Foundation of China (No. 12201643) and Natural Science Foundation of Hunan Province, China (No. 2023JJ40690). The second author was supported in part by Taiwan’s MoST grant 110-2115-M-001-009-MY3.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**377**(2024), 4961-4991 - MSC (2020): Primary 30D35; Secondary 11J97, 30A99
- DOI: https://doi.org/10.1090/tran/9175