Geodesic
Codimension 1 subvarieties $\scr M\sb g$ and real gonality of real curves
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 917-924 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 ${\mathbb {R}}$.
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 ${\mathbb {R}}$.
Classification : 14H10, 14H51, 14P99
Keywords: moduli space of curves; gonality; real curves; Brill-Noether theory; real algebraic curves; real Riemann surfaces 
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Ballico, E. Codimension 1 subvarieties $\scr M\sb g$ and real gonality of real curves. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 917-924. http://geodesic.mathdoc.fr/item/CMJ_2003_53_4_a10/

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