**
Czechoslovak Mathematical Journal, Vol. 53, No. 4, pp. 917-924, 2003
**

#
Codimension 1 subvarieties of $\Cal{M}_g$ and

real gonality of real curves

##
E. Ballico

**Abstract:** 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 ${\bb{R}}$, then there exists a low degree pencil $u X \to{\bb{P}}^1$ defined over ${\bb{R}}$.

**Keywords:** moduli space of curves, gonality, real curves, Brill-Noether theory, real algebraic curves, real Riemann surfaces

**Classification (MSC 2000):** 14H10, 14H51, 14P99

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