# Positivity of anticanonical divisors from the viewpoint of Fano conic bundles

## TL;DR

This paper presents the first examples of Fano manifolds with flat fiber type contractions onto non-weak Fano varieties, demonstrating these are Fano conic bundles and reviewing related positivity properties.

## Contribution

It provides the first known examples of such contractions and clarifies their structure as Fano conic bundles, expanding understanding of anticanonical divisor positivity.

## Key findings

- First examples of flat fiber type contractions onto non-weak Fano varieties.
- These contractions are proven to be Fano conic bundles.
- Review of known results on anticanonical divisor positivity.

## Abstract

We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between the positivity properties of anticanonical divisors of varieties of contractions.