Smooth complex projective rational surfaces with infinitely many real forms

TL;DR

This paper constructs a smooth complex projective rational surface with infinitely many non-isomorphic real forms, answering a long-standing open question in algebraic geometry.

Contribution

It provides the first explicit example of a rational surface with infinitely many real forms, resolving a major open problem.

Findings

Existence of a rational surface with infinitely many real forms

First explicit example addressing the open question

Advances understanding of real forms of algebraic surfaces

Abstract

We construct a smooth complex projective rational surface with infinitely many mutually non-isomorphic real forms. This gives the first definite answer to a long standing open question if a smooth complex projective rational surface has only finitely many non-isomorphic real forms or not.