Holomorphic Curves into Algebraic Varieties Intersecting Divisors in Subgeneral Position

TL;DR

This paper advances the second main theorem for holomorphic curves intersecting divisors in algebraic varieties by introducing the index of subgeneral position, leading to improved results and applications to Diophantine approximation.

Contribution

It introduces the concept of the index of subgeneral position, refining existing notions and improving second main theorem results for holomorphic curves.

Findings

Improved second main theorem results for holomorphic curves

Introduction of the index of subgeneral position

Establishment of Schmidt's subspace theorems analogues

Abstract

Recently, there are many developments on the second main theorem for holomorphic curves into algebraic varieties intersecting divisors in general position or subgeneral position. In this paper, we refine the concept of subgeneral position by introducing the notion of the index of subgeneral position. With this new notion we give some surprising improvement of the previous known second main theorem type results. Moreover, via the analogue between Nevanlinna theory and Diophantine approximation, the corresponding Schmidt's subspace type theorems are also established in the final section.