1. Codimension 1 subvarieties $\scr M\sb g$ and real gonality of real curves
- Creator:
- Ballico, Edoardo
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- moduli space of curves, gonality, real curves, Brill-Noether theory, real algebraic curves, and real Riemann surfaces
- Language:
- English
- Description:
- Let ${\mathcal{M}}_g$ be the moduli space of smooth complex projective curves of genus $g$. Here we prove that the subset of ${\mathcal{M}}_g$ formed by all curves for which some Brill-Noether locus has dimension larger than the expected one has codimension at least two in ${\mathcal{M}}_g$. As an application we show that if $X \in {\mathcal{M}}_g$ is defined over ${\mathbb {R}}$, then there exists a low degree pencil $u\: X \rightarrow {\mathbb {P}}^1$ defined over ${\mathbb {R}}$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public