Real forms on rational surfaces

TL;DR

This paper constructs rational surfaces with arbitrarily many distinct real forms, demonstrating the diversity of real structures on complex algebraic surfaces.

Contribution

It introduces a method to explicitly construct rational surfaces with any prescribed number of non-isomorphic real forms.

Findings

Existence of rational surfaces with arbitrarily many real forms

Explicit construction techniques for real forms

Demonstration of non-isomorphic real structures

Abstract

For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.