# Varieties with nef diagonal

## TL;DR

This paper investigates when the diagonal of a smooth projective variety is nef, providing classifications for certain varieties and exploring the nefness in spherical varieties.

## Contribution

It classifies complete intersections and smooth del Pezzo varieties with nef diagonals and studies the nefness in spherical varieties.

## Key findings

- Complete intersections with nef diagonal are classified.
- Smooth del Pezzo varieties with nef diagonal are classified.
- Nefness of the diagonal is analyzed for spherical varieties.

## Abstract

For a smooth projective variety $X$, we consider when the diagonal $\Delta_X$ is nef as a cycle on $X\times X$. In particular, we give a classification of complete intersections and smooth del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for spherical varieties.