Maximalite des varietes toriques de dimension 4

TL;DR

This paper proves that all 4-dimensional toric varieties over the reals are maximal, meaning their Betti numbers match those of their real parts, highlighting a significant topological property.

Contribution

The paper establishes that toric varieties of dimension 4 are maximal, a new result in the topology of real algebraic varieties.

Findings

4-dimensional toric varieties are maximal over the reals

Betti numbers of these varieties match those of their real parts

Advances understanding of topological properties of real algebraic varieties

Abstract

A complex algebraic variety defined over the reals is maximal when the sum of its Betti numbers for Borel Moore homology with $\zz$ coefficients coincides with the sum of the Betti numbers of its real part. We will show in this paper that toric varieties of dimension 4 are maximal.