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

Dept. of Mathematics, University of Trento, 38050 Povo (TN), Italy, e-mail: ballico@science.unitn.it

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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