Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SECOND MAIN THEOREM FOR HOLOMORPHIC CURVES INTO ALGEBRAIC VARIETIES WITH THE MOVING TARGETS ON AN ANGULAR DOMAIN

  • Chen, Jiali (Department of Mathematics Renmin University of China) ;
  • Zhang, Qingcai (Department of Mathematics Renmin University of China)
  • Received : 2021.09.14
  • Accepted : 2022.05.02
  • Published : 2022.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we will prove the second main theorem for holomorphic curves intersecting the moving hypersurfaces in subgeneral position with index on an angular domain. Our results are an extension of the previous second main theorems for holomorphic curves with moving targets on an angular domain.

Keywords

Acknowledgement

The authors thank the referees for their suggestions and comments that improved the quality of the paper.

References

  1. H. Cartan, Sur les zeros des combinaisons lineaires de p fonctions holomorphes donnees, Mathematica (Cluj) 7 (1933), 5-31.
  2. J. L. Chen, The Second Main Theorem for Holomorphic Mappings Sharing Moving Targets, Master's Thesis, Nanchang University, 2018.
  3. G. Dethloff and T. V. Tan, A second main theorem for moving hypersurface targets, Houston J. Math. 37 (2011), no. 1, 79-111.
  4. G. Dethloff and T. V. Tan, Holomorphic curves into algebraic varieties intersecting moving hypersurface targets, Acta Math. Vietnam. 45 (2020), no. 1, 291-308. https://doi.org/10.1007/s40306-019-00336-3
  5. D. Drasin and W. K. Hayman, Value distribution of functions meromorphic in an angle, Proc. London Math. Soc. (3) 48 (1984), no. 2, 319-340. https://doi.org/10.1112/plms/s3-48.2.319
  6. A. A. Goldberg and I. V. Ostrovskii, Value distribution of meromorphic functions, translated from the 1970 Russian original by Mikhail Ostrovskii, Translations of Mathematical Monographs, 236, American Mathematical Society, Providence, RI, 2008. https://doi.org/10.1090/mmono/236
  7. Q. Ji, Q. Yan, and G. Yu, Holomorphic curves into algebraic varieties intersecting divisors in subgeneral position, Math. Ann. 373 (2019), no. 3-4, 1457-1483. https://doi.org/10.1007/s00208-018-1661-4
  8. R. Nevanlinna, Zur Theorie der Meromorphen Funktionen, Acta Math. 46 (1925), no. 1-2, 1-99. https://doi.org/10.1007/BF02543858
  9. E. I. Nochka, On the theory of meromorphic curves, Sov. Math. Dokl. 27 (1983), no. 2, 377-381.
  10. S. D. Quang, Second main theorem for meromorphic mappings with moving hypersurfaces in subgeneral position, J. Math. Anal. Appl. 465 (2018), no. 1, 604-623. https://doi.org/10.1016/j.jmaa.2018.05.027
  11. M. Ru, On a general form of the second main theorem, Trans. Amer. Math. Soc. 349 (1997), no. 12, 5093-5105. https://doi.org/10.1090/S0002-9947-97-01913-2
  12. M. Ru, A defect relation for holomorphic curves intersecting hypersurfaces, Amer. J. Math. 126 (2004), no. 1, 215-226. https://doi.org/10.1353/ajm.2004.0006
  13. M. Ru, Holomorphic curves into algebraic varieties, Ann. of Math. (2) 169 (2009), no. 1, 255-267. https://doi.org/10.4007/annals.2009.169.255
  14. M. Ru and W. Stoll, The second main theorem for moving targets, J. Geom. Anal. 1 (1991), no. 2, 99-138. https://doi.org/10.1007/BF02938116
  15. M. Ru and J. T.-Y. Wang, Truncated second main theorem with moving targets, Trans. Amer. Math. Soc. 356 (2004), no. 2, 557-571. https://doi.org/10.1090/S0002-9947-03-03453-6
  16. N. V. Thin, On Nevanlinna-Cartan theory for holomorphic curves with Tsuji characteristics, arXiv:1706.05896V2 [math.CV].
  17. M. Tsuji, Potential Theory in Modern Function Theory, Maruzen Co. Ltd., Tokyo, 1959.
  18. L. Xie and T. Cao, Second main theorem for meromorphic maps into algebraic varieties intersecting moving hypersurfaces targets, Chinese Ann. Math. Ser. B 42 (2021), no. 5, 753-776. https://doi.org/10.1007/s11401-021-0289-y
  19. J. Zheng, On transcendental meromorphic functions with radially distributed values, Sci. China Ser. A 47 (2004), no. 3, 401-416. https://doi.org/10.1360/02ys0210
  20. J. Zheng, Value distribution of holomorphic curves on an angular domain, Michigan Math. J. 64 (2015), no. 4, 849-879. https://doi.org/10.1307/mmj/1447878034