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arXiv · 2310.18086

Four families of maximal real algebraic hypersurfaces in $\mathbb{RP}^4$

Aloïs Demory
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Abstract

In this paper, we present four families of maximal real algebraic hypersurfaces of even degree in $\mathbb{RP}^4$ 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 $\mathbb{CP}^4$ 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.

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Aloïs Demory. 2023-10-27. Four families of maximal real algebraic hypersurfaces in $\mathbb{RP}^4$. https://arxiv.org/abs/2310.18086

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