Schmidt's subspace theorem for moving hypersurface targets in subgeneral position with index in algebraic variety

TL;DR

This paper extends Schmidt's Subspace Theorem to moving hypersurface targets in subgeneral position with index intersecting algebraic varieties, building on recent advances and methods from multiple researchers.

Contribution

It introduces a new version of Schmidt's Subspace Theorem for moving hypersurfaces in subgeneral position with index intersecting algebraic varieties, extending prior results.

Findings

Extended Schmidt's Subspace Theorem to new geometric configurations

Incorporated methods from Son-Tan-Thin, Quang, and Xie-Cao

Provided a broader framework for value distribution in algebraic geometry

Abstract

Recently, Xie-Cao [15] obtained a Second Main Theorem for moving hypersurfaces located in subgeneral position with index which is extended the result of Ru [11]. By using some methods due to Son-Tan-Thin [13], Quang [9] and Xie-Cao [15], we shall give a Schmidt's Subspace Theorem for moving hypersurface targets in subgeneral position with index intersecting algebraic variety. Our result is a extension the Schmidt's Subspace Theorem due to Son-Tan-Thin [13] and Quang [9].