Nombres de Betti des surfaces elliptiques r\'{e}elles

TL;DR

This paper establishes a new bound on the number of connected components of real regular elliptic surfaces with a section, demonstrates its sharpness, and characterizes all possible Betti number values for these surfaces.

Contribution

It introduces a new bound for the Betti numbers of real regular elliptic surfaces and proves its optimality, while also classifying all attainable Betti number configurations.

Findings

New sharp bound for the number of connected components

All Betti number values for such surfaces are realized

The bound is proven to be optimal

Abstract

We prove a new bound for the number of connected components of a real regular elliptic surface with a real section and we show the sharpness of this bound. Furthermore, all possible values for the Betti numbers of such a surface are realized.