Codimension 1 subvarieties ℳ g and real gonality of real curves

Edoardo Ballico

Czechoslovak Mathematical Journal (2003)

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

Abstract

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Let ℳ g be the moduli space of smooth complex projective curves of genus g . Here we prove that the subset of 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 ℳ g . As an application we show that if X ∈ ℳ g is defined over ℝ , then there exists a low degree pencil u X → ℙ 1 defined over ℝ .

How to cite

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Ballico, 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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  8. 10.1007/BF01393371, Invent. Math. 67 (1982), 23–86. (1982) MR0664324DOI10.1007/BF01393371
  9. Separable gonality of a Gorenstein curve, Mat. Contemp (to appear). (to appear) Zbl0921.14014MR1663640
  10. Teichmüller spaces of Klein surfaces, Ann. Acad. Sci. Fenn. Ser. A I. Math. Dissertationes 15 (1978), 1–37. (1978) 
  11. Real algebraic curves in the moduli spaces of complex curves, Compositio Math. 74 (1990), 259–283. (1990) MR1055696
  12. Fibrés vectoriels sur les courbes algébriques. Astérisque 96, Soc. Math. France, 1982. (1982) MR0699278

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