| Title:
|
Codimension 1 subvarieties $\scr M\sb g$ and real gonality of real curves (English) |
| Author:
|
Ballico, E. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
917-924 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 ${\mathbb {R}}$. (English) |
| Keyword:
|
moduli space of curves |
| Keyword:
|
gonality |
| Keyword:
|
real curves |
| Keyword:
|
Brill-Noether theory |
| Keyword:
|
real algebraic curves |
| Keyword:
|
real Riemann surfaces |
| MSC:
|
14H10 |
| MSC:
|
14H51 |
| MSC:
|
14P99 |
| idZBL:
|
Zbl 1080.14518 |
| idMR:
|
MR2018839 |
| . |
| Date available:
|
2009-09-24T11:07:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127849 |
| . |
| Reference:
|
[1] E. Arbarello, M. Cornalba, P. Griffiths and J. Harris: Geometry of Algebraic Curves, I .Springer-Verlag, 1985. MR 0770932 |
| Reference:
|
[2] S. Chaudary: The Brill-Noether theorem for real algebraic curves. Ph.D. thesis.Duke University, 1995. |
| Reference:
|
[3] M. Coppens: One-dimensional linear systems of type II on smooth curves. Ph.D. thesis.Utrecht, 1983. |
| Reference:
|
[4] M. Coppens and G. Martens: Linear series on a general $k$-gonal curve.Abh. Math. Sem. Univ. Hamburg 69 (1999), 347–371. MR 1722944, 10.1007/BF02940885 |
| Reference:
|
[5] S. Diaz: A bound on the dimension of complete subvarieties of ${\mathcal{M}}_g$.Duke Math. J. 51 (1984), 405–408. MR 0747872, 10.1215/S0012-7094-84-05119-6 |
| Reference:
|
[6] C. J. Earle: On moduli of closed Riemann surfaces with symmetries.Advances in the Theory of Riemann Surfaces. Annals of Math. Studies 66, Princeton, N. J., 1971, pp. 119–130. MR 0296282 |
| Reference:
|
[7] B. Gross and J. Harris: Real algebraic curves.Ann. scient. Éc. Norm. Sup., $4^e$ série 14 (1981), 157–182. MR 0631748 |
| Reference:
|
[8] J. Harris and D. Mumford: On the Kodaira dimension of the moduli space of curves.Invent. Math. 67 (1982), 23–86. MR 0664324, 10.1007/BF01393371 |
| Reference:
|
[9] M. Homma: Separable gonality of a Gorenstein curve.Mat. Contemp (to appear). Zbl 0921.14014, MR 1663640 |
| Reference:
|
[10] M. Seppälä: Teichmüller spaces of Klein surfaces.Ann. Acad. Sci. Fenn. Ser. A I. Math. Dissertationes 15 (1978), 1–37. |
| Reference:
|
[11] M. Seppälä: Real algebraic curves in the moduli spaces of complex curves.Compositio Math. 74 (1990), 259–283. MR 1055696 |
| Reference:
|
[12] C. S. Seshadri: Fibrés vectoriels sur les courbes algébriques. Astérisque 96.Soc. Math. France, 1982. MR 0699278 |
| . |
