# Criteria for complete intersections

## TL;DR

This paper develops criteria to identify complete intersections in projective varieties, focusing on subvarieties of rational homogeneous varieties and addressing Hartshorne's conjecture.

## Contribution

It provides new criteria for detecting complete intersections and explores conditions for subvarieties to be complete intersections in specific geometric contexts.

## Key findings

- Criteria for complete intersections in projective varieties
- Conditions under which subvarieties are complete intersections
- Insights into Hartshorne's conjecture for rational homogeneous varieties

## Abstract

We obtain criteria for detecting complete intersections in projective varieties. Motivated by a conjecture of Hartshorne concerning subvarieties of projective spaces, we investigate situations when two-codimensional smooth subvarieties of rational homogeneous varieties are complete intersections.