Year: 2013
Type: preprint
Abstract: We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections are transverse. In particular, under a transversality assumption, if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are hypersurfaces of degree d, we prove the defect relation \sum_{i=1}^qδ_f(D_i)\leq n-1+1/d, which is sharp for all positive integers n and d.
Source: arXiv (Cornell University)
Author: Levin, Aaron
Institution: Michigan State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951320326