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A new degenerated second main theorem for meromorphic mappings with hypersurfaces
Abstract
We establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into a projective variety and a family of hypersurfaces in subgeneral position. The above bound of the total defect obtained from our result is better than that of the previous results. Moreover, in our result, the truncation level of the counting functions is estimated explicitly and independently of the number of hypersurfaces. Especially, we do not need the assumption that the family of hypersurfaces must satisfy the Bezout properties as imposed in some earlier studies, but only a weak Bezout property.
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BibTeX
@misc{dethloff2026degenerated,
title = {{A new degenerated second main theorem for meromorphic mappings with hypersurfaces}},
author = {Gerd Dethloff and Si Duc Quang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17142},
eprint = {2609.17142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17142},
}
RIS
TY - UNPB
TI - A new degenerated second main theorem for meromorphic mappings with hypersurfaces
AU - Gerd Dethloff
AU - Si Duc Quang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17142
UR - https://arxiv.org/abs/2609.17142
AB - We establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into a projective variety and a family of hypersurfaces in subgeneral position. The above bound of the total defect obtained from our result is better than that of the previous results. Moreover, in our result, the truncation level of the counting functions is estimated explicitly and independently of the number of hypersurfaces. Especially, we do not need the assumption that the family of hypersurfaces must satisfy the Bezout properties as imposed in some earlier studies, but only a weak Bezout property.
ER -