# On the deformation rigidity of smooth projective symmetric varieties with Picard number one

## TL;DR

This paper investigates the deformation rigidity of smooth projective symmetric varieties with Picard number one, focusing on their behavior under Kähler deformations within the context of spherical and symmetric varieties.

## Contribution

It provides new insights into the deformation rigidity of a specific class of symmetric varieties, expanding understanding of their stability under Kähler deformations.

## Key findings

- Identifies conditions for rigidity of symmetric varieties
- Shows rigidity results for varieties with Picard number one
- Contributes to classification of symmetric varieties under deformation

## Abstract

Symmetric varieties are normal equivariant open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. The principal goal of this article is to study the rigidity under K\"{a}hler deformations of smooth projective symmetric varieties with Picard number one.