Algebroid Mappings and Their Equidistribution Theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908705178517504 |
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| author | Dong, Xianjing |
| author_facet | Dong, Xianjing |
| contents | In this paper, the concept of algebroid mappings of complex manifolds is introduced based on that a large number of complex systems of PDEs admit multi-valued solutions that can be defined by a system of independent algebraic equations over the field of meromorphic functions. It is well-known that Nevanlinna theory is an important tool in complex ODE theory. To develop a similar tool applied to the study of algebroid solutions of complex systems of PDEs, one explores the equidistribution theory of algebroid mappings. Via uniformizating an algebroid mapping, we obtain a second main theorem of algebroid mappings from a complete Kähler manifold into a complex projective manifold provided that some certain conditions are imposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebroid Mappings and Their Equidistribution Theory Dong, Xianjing Complex Variables In this paper, the concept of algebroid mappings of complex manifolds is introduced based on that a large number of complex systems of PDEs admit multi-valued solutions that can be defined by a system of independent algebraic equations over the field of meromorphic functions. It is well-known that Nevanlinna theory is an important tool in complex ODE theory. To develop a similar tool applied to the study of algebroid solutions of complex systems of PDEs, one explores the equidistribution theory of algebroid mappings. Via uniformizating an algebroid mapping, we obtain a second main theorem of algebroid mappings from a complete Kähler manifold into a complex projective manifold provided that some certain conditions are imposed. |
| title | Algebroid Mappings and Their Equidistribution Theory |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2506.07887 |