On images of weak Fano manifolds II

TL;DR

This paper provides a Hodge theoretic proof that the nefness of the anti-canonical divisor is preserved under smooth surjective morphisms between smooth complex projective varieties, without using mod p reduction.

Contribution

It offers a new proof technique for a known fact in algebraic geometry, avoiding mod p reduction and adding commentary on related work.

Findings

Anti-canonical divisor nefness is preserved under certain morphisms

Hodge theoretic methods can replace mod p arguments in this context

The approach simplifies understanding of weak Fano manifolds

Abstract

We consider a smooth projective surjective morphism between smooth complex projective varieties. We give a Hodge theoretic proof of the following well-known fact: If the anti-canonical divisor of the source space is nef, then so is the anti-canonical divisor of the target space. We do not use mod $p$ reduction arguments. In addition, we make some supplementary comments on our paper: On images of weak Fano manifolds.