A note about rational surfaces as unions of affine planes

TL;DR

This paper proves that every smooth rational projective surface over the complex numbers can be covered by three affine planes, providing a new understanding of their geometric structure.

Contribution

It establishes that such surfaces can be decomposed into three affine plane subsets, a novel result in the study of rational surfaces.

Findings

Any smooth rational projective surface over complex numbers has an open cover by three affine planes.

This decomposition offers new insights into the structure of rational surfaces.

The result simplifies the understanding of the geometry of these surfaces.

Abstract

We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.