# A note on flatness of some fiber type contractions

## TL;DR

This paper investigates the flatness of certain fiber type contractions in complex smooth projective varieties, exploring their relation to conic bundle structures and considering cases with mild singularities.

## Contribution

It provides new insights into the flatness properties of fiber type contractions and their connection to conic bundle structures, even in the presence of mild singularities.

## Key findings

- Flatness of some fiber type contractions is characterized.
- Relation between flatness and conic bundle structures established.
- Results extend to varieties with mild singularities.

## Abstract

We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures, also in the general case in which some mild singularities of the varieties are admitted.