arXiv subjects

Aloïs Demory

Publications and source records attributed to Aloïs Demory.

3 recordsLinked to original sources

arXiv2026

Non-existence of separating morphisms of low degree

A separating curve is a real curve whose real part disconnects its complex part. It also admits totally real morphisms to the projective line, and the separating gonality is the minimal possible degree for such morphisms. The separating gonality is bounded from below by the number of connected components of the real part of the curve. In this paper, we build on a strategy of Manzaroli to improve this lower bound for some curves embedded in the projective plane or in a Hirzebruch surface.

math.AG↗

arXiv2026

Real critical points of $T$-polynomials that are sums of squared monomials and topology of $T$-hypersurfaces

We study the topology of the real algebraic hypersurfaces in $\mathbb{P}^n$ that can be constructed via combinatorial patchworking using triangulations that are dilations by two of other triangulations. By examining the real critical points of the polynomials that define such hypersurfaces, we find some asymptotical upper bounds on various sums of their Betti numbers. We then discuss the sharpness of those bounds.

math.AG↗

arXiv2023

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

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.

math.AG↗