Varieties with nef anticanonical divisors and Albanese morphisms of relative dimension one in positive characteristic

TL;DR

This paper investigates the structure of smooth projective varieties with nef anticanonical divisors over fields of positive characteristic, focusing on cases where the Albanese morphism has relative dimension one, revealing new structural insights.

Contribution

It provides a detailed description of such varieties' structure when the Albanese morphism has relative dimension one in positive characteristic.

Findings

Characterization of varieties with nef anticanonical divisors in positive characteristic

Structural results for Albanese morphisms of relative dimension one

New insights into the geometry of varieties in positive characteristic

Abstract

Let $X$ be a smooth projective variety with a nef anticanonical divisor over an algebraically closed field of characteristic $p>0$. In this paper, we establish a precise structure of $X$ under the condition that $a_X: X \to {\rm Alb}(X)$ is of relative dimension one.