# Invariants of Fano varieties in families

## TL;DR

This paper proves that the Picard rank remains constant in families of Fano varieties across all characteristics and explores the conditions under which the index is also constant.

## Contribution

It establishes the invariance of Picard rank in families of Fano varieties and investigates the constancy of the index, extending known results to arbitrary characteristic.

## Key findings

- Picard rank is constant in families of Fano varieties
- Index constancy is analyzed in the context of these families
- Results hold in arbitrary characteristic

## Abstract

We show that the Picard rank is constant in families of Fano varieties (in arbitrary characteristic) and we moreover investigate the constancy of the index.