# Second main theorem for holomorphic curves into algebraic varieties intersecting moving hypersurfaces targets

## TL;DR

This paper improves Ru's second main theorem for holomorphic curves intersecting moving hypersurfaces in algebraic varieties, especially when these hypersurfaces are in subgeneral position with an index, advancing the understanding of value distribution theory.

## Contribution

It provides new enhancements to Ru's second main theorem for moving hypersurfaces in subgeneral position, broadening its applicability and depth.

## Key findings

- Enhanced second main theorem for moving hypersurfaces in subgeneral position
- Broader conditions under which the theorem applies
- Improved bounds on intersection multiplicities

## Abstract

Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009, recently there has been some developments on the second main theorem into algebraic varieties intersecting moving hypersurfaces targets. The main purpose of this paper is to give some interesting improvements of Ru's second main theorem for moving hypersurfaces targets located in subgeneral position with index.