# Vinberg's X_4 Revisited

## TL;DR

This paper revisits Vinberg's work on a special complex K3 surface with maximal Picard rank and discriminant four, exploring its automorphisms and geometric properties.

## Contribution

It provides a geometric perspective on Vinberg's results by identifying automorphism generators via Cremona transformations.

## Key findings

- Identifies generators of the automorphism group of the K3 surface.
- Describes the structure of smooth rational curves on the surface.
- Connects automorphisms to Cremona transformations of the projective plane.

## Abstract

The article covers the unique complex K3 surface with maximal Picard rank and discriminant four. We discuss smooth, rational curves and identify generators of its automorphism group with certain Cremona transformations of $\mathbb{P}^2$. This gives a geometric perspective of Vinberg's results.