On the gonality of curves in 𝐏 n

Edoardo Ballico

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 177-186
  • ISSN: 0010-2628

Abstract

top
Here we study the gonality of several projective curves which arise in a natural way (e.gċurves with maximal genus in 𝐏 n , curves with given degree d and genus g for all possible d , g if n = 3 and with large g for arbitrary ( d , g , n ) ).

How to cite

top

Ballico, Edoardo. "On the gonality of curves in $\mathbf {P}^n$." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 177-186. <http://eudml.org/doc/248095>.

@article{Ballico1997,
abstract = {Here we study the gonality of several projective curves which arise in a natural way (e.gċurves with maximal genus in $\mathbf \{P\}^n$, curves with given degree $d$ and genus $g$ for all possible $d$, $g$ if $n = 3$ and with large $g$ for arbitrary $(d,g,n)$).},
author = {Ballico, Edoardo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {space curve; algebraic curve; projective curve; gonality; algebraic surface; space curve; Clifford index; gonality},
language = {eng},
number = {1},
pages = {177-186},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the gonality of curves in $\mathbf \{P\}^n$},
url = {http://eudml.org/doc/248095},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Ballico, Edoardo
TI - On the gonality of curves in $\mathbf {P}^n$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 177
EP - 186
AB - Here we study the gonality of several projective curves which arise in a natural way (e.gċurves with maximal genus in $\mathbf {P}^n$, curves with given degree $d$ and genus $g$ for all possible $d$, $g$ if $n = 3$ and with large $g$ for arbitrary $(d,g,n)$).
LA - eng
KW - space curve; algebraic curve; projective curve; gonality; algebraic surface; space curve; Clifford index; gonality
UR - http://eudml.org/doc/248095
ER -

References

top
  1. Arbarello E., Cornalba M., Footnotes to a paper of Beniamino Segre, Math. Ann. 256 (1981), 341-362. (1981) Zbl0454.14023MR0626954
  2. Arbarello E., Cornalba M., Griffiths Ph., Harris J., Geometry of Algebraic Curves, I, Springer-Verlag, 1985. MR0770932
  3. Ballico E., On the gonality of nodal curves, Geom. Dedicata 37 (1991), 357-360. (1991) Zbl0716.14013MR1094698
  4. Beltrametti M., Francia P., Sommese A.J., On Reider's method and higher order embeddings, Duke Math. J. 58 (1989), 425-439. (1989) Zbl0702.14010MR1016428
  5. Ciliberto C., Hilbert functions of finite sets of points and the genus of a curve in a projective space, in: Space Curves, pp.24-73, Lect. Notes in Math. 1266, Springer-Verlag, 1987. Zbl0625.14016MR0908707
  6. Ciliberto C., 0n the degree and genus of smooth curves in a projective space, Adv. Math. 81 (1990), 198-248. (1990) MR1055647
  7. Coppens M., Kato T., The gonality of smooth curves with plane models, Manuscripta Math. 70 (1990), 5-25. (1990) Zbl0725.14005MR1080899
  8. Coppens M., Martens G., Secant spaces and Clifford's theorem, Compositio Math. 78 (1991), 1-22. (1991) Zbl0741.14035MR1104787
  9. Gruson L., Peskine Ch., Genre de courbes de l'espace projectif, II, Ann. Sci. Ecole Norm. Sup. (4) 15 (1982), 401-418. (1982) MR0690647
  10. Harris J., Eisenbud D., Curves in a projective space, Les presses de l'Université de Montreal, 1982. MR0685427
  11. Hartshorne R., Algebraic Geometry, Springer-Verlag, 1977. Zbl0531.14001MR0463157
  12. Hartshorne R., Genre des courbes algébriques dans l'espace projectif (d'après L. Gruson et C. Peskine), in: Séminaire Bourbaki 1981/82, exp.592, pp.301-313, Astérisque 92-93, 1982. Zbl0524.14037MR0689536
  13. Mori S., On the degree and genera of curves on smooth quartic surfaces in 𝐏 3 , Nagoya Math. J. 69 (1984), 127-132. (1984) MR0771073
  14. Rathmann J., The genus of curves in 𝐏 4 and 𝐏 5 , Math. Z. 202 (1989), 525-543. (1989) MR1022819
  15. Shepherd-Barrow N.I., Unstable vector bundles and linear systems on surfaces in characteristic p , Invent. Math. 106 (1991), 243-262. (1991) MR1128214

NotesEmbed ?

top

You must be logged in to post comments.