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 $\mc{D}$ 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 $|\mc{D}|$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1708.08400
- arXiv:
- arXiv:1708.08400
- Bibcode:
- 2017arXiv170808400B
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Combinatorics;
- 14C20;
- 14N10;
- 14P25;
- 14Hxx;
- 14Txx
- E-Print:
- v.2: improved exposition following the referee's suggestions, and included a new result (Thm 6.1) giving a more refined construction of real inflection on complete series on hyperelliptic curves that includes non-maximal cases. To appear in Transactions of the AMS