Real inflection points of real hyperelliptic curves

Abstract:

Given a real hyperelliptic algebraic curve $X$ with non-empty real part and a real effective divisor $\mathcal {D}$ arising via pullback from $\mathbb {P}^1$ under the hyperelliptic structure map, we study the real inflection points of the associated complete real linear series $|\mathcal {D}|$ on $X$.

To do so we use Viro’s patchworking of real plane curves, recast in the context of some Berkovich spaces studied by M. Jonsson. Our method gives a simpler and more explicit alternative to limit linear series on metrized complexes of curves, as developed by O. Amini and M. Baker, for curves embedded in toric surfaces.