|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Generalizations of
degeneracy second main theorem and Schmidt's subspace
theorem
Si Duc Quang |
|
Vol. 318 (2022), No. 1, 153–188
|
|
DOI: 10.2140/pjm.2022.318.153
|
Abstract |
|
By introducing the notion of distributive constant of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary families of hypersurfaces. Our second main theorem generalizes and improves previous results for meromorphic mappings with hypersurfaces, in particular for algebraically nondegenerate mappings with hypersurfaces in subgeneral position. The analogous results for the holomorphic curves with finite growth index from a complex disc into a projective variety, and for meromorphic mappings on a complete Kähler manifold are also given. For the last aim, we will prove a Schmidt’s subspace theorem for arbitrary families of homogeneous polynomials, which is the counterpart in the number theory of our second main theorem. |
PDF Access Denied
We have not been able to recognize your IP address
3.143.244.83
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
Nevanlinna theory, diophantine approximation, second main
theorem, subspace theorem, meromorphic mapping,
hypersurface, homogeneous polynomial, subgeneral position
|
Mathematical Subject Classification
Primary: 11J68, 32H30
Secondary: 11J25, 30D35, 32A22
|
Milestones
Received: 23 January 2022
Revised: 13 March 2022
Accepted: 9 April 2022
Published: 1 August 2022
|
Authors |
| Si Duc Quang | |
| Department of Mathematics Hanoi National University of Education 136-Xuan Thuy, Cau Giay Hanoi Vietnam |
Thang Long Institute of Mathematics
and Applied Sciences (TIMAS) Thang Long University Nghiem Xuan Yem, Hoang Mai Hanoi Vietnam |
