Logarithmic bounds on Fujita's conjecture

TL;DR

This paper establishes bounds on Fujita's basepoint freeness conjecture for smooth complex projective varieties, showing they grow proportionally to n log log n, which advances understanding of the conjecture's limitations.

Contribution

The paper provides new bounds on Fujita's conjecture that grow as n log log n, improving previous known bounds and offering insights into the conjecture's behavior.

Findings

Bounds grow as n log log n

Advances understanding of Fujita's conjecture

Provides new theoretical limits

Abstract

Let X be a smooth complex projective variety of dimension n. We prove bounds on Fujita's basepoint freeness conjecture that grow as nloglog(n).