Real del Pezzo surfaces without points

TL;DR

This paper studies real del Pezzo surfaces lacking real points and proves that their complex counterparts have a Picard number of at least two, revealing a link between real and complex geometric properties.

Contribution

It establishes a lower bound on the Picard number of complex del Pezzo surfaces associated with real surfaces without points, a novel connection in algebraic geometry.

Findings

Real del Pezzo surfaces without points exist.

Their complex counterparts have Picard number ≥ 2.

The result links real and complex geometric properties.

Abstract

We consider a real del Pezzo surface without points. We prove that the same surface over complex numbers field $\mathbb{C}$ has Picard number is at least two.