Four families of maximal real algebraic hypersurfaces in \mathbbRP⁴

2023/10/27 by Demory, Aloïs
Mathematics · Engineering · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2310.18086

Abstract

In this paper, we present four families of maximal real algebraic hypersurfaces of even degree in \mathbbRP⁴ constructed using O. Viro's combinatorial patchworking method. We compare the Euler characteristic of the real part and the signature of the complex part of double coverings of \mathbbCP⁴ ramified over the complex part of the constructed real algebraic hypersurfaces. We prove that these invariants are not necessarily equal and can even be asymptotically different.

Related

• Patchworking real algebraic varieties
• Euler characteristic of primitive T-hypersurfaces and maximal surfaces
• Real algebraic surfaces with many handles in (\mathbbCP¹)³
• Complex conjugation and simplicial algebraic hypersurfaces
• Asymptotiques de nombres de Betti d'hypersurfaces projectives réelles