# Codimension one Fano distributions on Fano manifolds

## TL;DR

This paper classifies codimension one Fano distributions on Fano manifolds with Picard number one, including their moduli spaces, focusing on maximal index cases and specific varieties like complete intersections and Grassmannians.

## Contribution

It provides a comprehensive classification of codimension one Fano distributions on certain Fano manifolds, expanding understanding of their structure and moduli.

## Key findings

- Classification of Fano distributions of maximal index on various Fano manifolds.
- Description of moduli spaces of these distributions.
- Identification of all codimension one del Pezzo distributions on Fano manifolds.

## Abstract

In this paper we investigate codimension one Fano distributions on Fano manifolds with Picard number one. We classify Fano distributions of maximal index on complete intersections in weighted projective spaces, Fano contact manifolds, Grassmannians of lines and their linear sections, and describe their moduli spaces. As a consequence, we obtain a classification of codimension one del Pezzo distributions on Fano manifolds with Picard number one.