A non-integrated hypersurface defect relation for meromorphic maps over complete K\"ahler manifolds into projective algebraic varieties

TL;DR

This paper establishes a new non-integrated defect relation for meromorphic maps from complete Kähler manifolds into projective algebraic varieties, with bounds depending only on specific geometric parameters, extending previous results.

Contribution

It introduces a defect relation where bounds depend solely on the number of hypersurfaces, their degrees, and the variety's dimension, generalizing earlier work by Fujimoto.

Findings

Derived a defect relation with bounds depending only on key parameters.

Recovers Fujimoto's theorem under similar conditions.

Applicable to hypersurfaces in k-subgeneral position.

Abstract

In this paper, a non-integrated defect relation for meromorphic maps from complete K\"ahler manifolds $M$ into smooth projective algebraic varieties $V$ intersecting hypersurfaces located in $k$-subgeneral position is proved. The novelty of this result lies in that both the upper bound and the truncation level of our defect relation depend only on $k$, $\dim_{\,\mathbb{C}}(V)$ and the degrees of the hypersurfaces considered. In addition, this defect relation recovers Hirotaka Fujimoto [Theorem 1.1; MR0884636 (88m:32049); Japan. J. Math. (N.S.) 11 (1985), no. 2, 233-264.] when subjected to the same conditions.