# Codimension 1 subvarieties ${\mathcal{M}}_{g}$ and real gonality of real curves

Czechoslovak Mathematical Journal (2003)

- Volume: 53, Issue: 4, page 917-924
- ISSN: 0011-4642

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topBallico, Edoardo. "Codimension 1 subvarieties $\mathcal {M}_g$ and real gonality of real curves." Czechoslovak Mathematical Journal 53.4 (2003): 917-924. <http://eudml.org/doc/30824>.

@article{Ballico2003,

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 $\{\mathbb \{R\}\}$, then there exists a low degree pencil $u\: X \rightarrow \{\mathbb \{P\}\}^1$ defined over $\{\mathbb \{R\}\}$.},

author = {Ballico, Edoardo},

journal = {Czechoslovak Mathematical Journal},

keywords = {moduli space of curves; gonality; real curves; Brill-Noether theory; real algebraic curves; real Riemann surfaces; moduli space of curves; gonality; real curves; Brill-Noether theory; real algebraic curves; real Riemann surfaces},

language = {eng},

number = {4},

pages = {917-924},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Codimension 1 subvarieties $\mathcal \{M\}_g$ and real gonality of real curves},

url = {http://eudml.org/doc/30824},

volume = {53},

year = {2003},

}

TY - JOUR

AU - Ballico, Edoardo

TI - Codimension 1 subvarieties $\mathcal {M}_g$ and real gonality of real curves

JO - Czechoslovak Mathematical Journal

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 53

IS - 4

SP - 917

EP - 924

AB - 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 ${\mathbb {R}}$.

LA - eng

KW - moduli space of curves; gonality; real curves; Brill-Noether theory; real algebraic curves; real Riemann surfaces; moduli space of curves; gonality; real curves; Brill-Noether theory; real algebraic curves; real Riemann surfaces

UR - http://eudml.org/doc/30824

ER -

## References

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