Effective non-vanishing of global sections of multiple adjoint bundles for polarized 4-folds

TL;DR

This paper investigates conditions under which the global sections of multiple adjoint bundles are non-zero on polarized 4-folds, contributing to the understanding of their geometric properties.

Contribution

It establishes criteria ensuring the non-vanishing of sections of m(K_X + L) for polarized 4-folds with non-negative Kodaira dimension.

Findings

Proves existence of m with h^0(m(K_X + L)) > 0 under certain conditions.

Provides new insights into the geometry of polarized 4-folds.

Advances non-vanishing theorems in higher-dimensional algebraic geometry.

Abstract

Let X be a smooth complex projective variety of dimension 4 and let L be an ample line bundle on X. In this paper, we study a natural number m such that h^{0}(m(K_{X}+L))>0 for any polarized 4-folds (X,L) with \kappa(K_{X}+L)\geq 0.