On Fujita's freeness conjecture in dimension 5

TL;DR

This paper proves that for a smooth projective 5-dimensional variety with an ample line bundle, the linear system |K_X + 6L| is base-point free, advancing Fujita's conjecture in dimension five.

Contribution

It establishes the base-point freeness of |K_X + 6L| for five-dimensional varieties, confirming a case of Fujita's conjecture.

Findings

|K_X + 6L| is base-point free for smooth 5-folds

Advances Fujita's freeness conjecture in dimension five

Provides new techniques for higher-dimensional algebraic geometry

Abstract

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$. We show that $|K_X + 6L|$ is base-point free.