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.

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.