Holomorphic curves into algebraic varieties intersecting moving hypersurface targets

TL;DR

This paper extends a second main theorem for holomorphic curves in complex projective varieties to include moving hypersurface targets, using a new proof method for the case of projective varieties.

Contribution

It generalizes previous results by incorporating moving hypersurfaces and introduces a novel proof technique for projective varieties.

Findings

Generalization of second main theorem to moving hypersurfaces

Introduction of a new proof method for projective varieties

Broader applicability in complex geometry

Abstract

In [Ann. of Math. 169 (2009)], Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method for the case of projective varieties, we generalize this result to moving hypersurface targets.