Strictly nef divisors on K-trivial fourfolds

TL;DR

This paper proves that strictly nef divisors on K-trivial fourfolds are ample, confirming the ampleness and Serrano's conjectures in this setting, which advances understanding of positivity properties on special algebraic varieties.

Contribution

The paper establishes the ampleness of strictly nef divisors on K-trivial fourfolds, confirming key conjectures in algebraic geometry for this class of varieties.

Findings

Strictly nef divisors on K-trivial fourfolds are ample.

Proof of the ampleness conjecture for these divisors.

Verification of Serrano's conjecture in this context.

Abstract

In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on projective fourfolds with trivial canonical bundle and vanishing irregularity are ample.