Dimension des familles de courbes lisses sur une surface quartique normale de
Author:
Sébastien Guffroy
Journal:
Proc. Amer. Math. Soc. 135 (2007), 3499-3505
MSC (2000):
Primary 14J17, 14N15
DOI:
https://doi.org/10.1090/S0002-9939-07-08966-6
Published electronically:
July 27, 2007
MathSciNet review:
2336563
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Dans cette note, on montre que les courbes, lisses connexes, de degré et genre
, tracées sur une surface quartique normale variable de
, et n'y étant pas intersection complète, forment des familles de dimensions
. Cette majoration est la meilleure possible. Comme application on prouve que le schéma de Hilbert des courbes lisses connexes de
de degré
et genre
est irréductible.
- 1. A. Dolcetti and G. Pareschi, On linearly normal space curves, Math. Z. 198 (1988), no. 1, 73–82. MR 938030, https://doi.org/10.1007/BF01183040
- 2. Philippe Ellia, D’autres composantes non réduites de 𝐻𝑖𝑙𝑏𝑃³, Math. Ann. 277 (1987), no. 3, 433–446 (French). MR 891584, https://doi.org/10.1007/BF01458324
- 3. Geir Ellingsrud and Stein Arild Strømme, Stable rank-2 vector bundles on 𝑃³ with 𝑐₁=0 and 𝑐₂=3, Math. Ann. 255 (1981), no. 1, 123–135. MR 611278, https://doi.org/10.1007/BF01450561
- 4. G. Gonzalez-Springer et M. Lejeune-Jalabert : Progress in Math., Vol 134 (1996) 9-31, Birkhaüser.
- 5. Laurent Gruson and Christian Peskine, Genre des courbes de l’espace projectif. II, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 3, 401–418 (French). MR 690647
- 6. Sébastien Guffroy, Sur l’incomplétude de la série linéaire caractéristique d’une famille de courbes planes à nœuds et à cusps, Nagoya Math. J. 171 (2003), 51–83 (French, with English and French summaries). MR 2002013, https://doi.org/10.1017/S0027763000025514
- 7. Henry B. Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977), no. 6, 1257–1295. MR 568898, https://doi.org/10.2307/2374025
- 8. Mireille Martin-Deschamps and Daniel Perrin, Sur la classification des courbes gauches, Astérisque 184-185 (1990), 208 (French). MR 1073438
- 9. Mireille Martin-Deschamps and Daniel Perrin, Courbes gauches et modules de Rao, J. Reine Angew. Math. 439 (1993), 103–145 (French). MR 1219697
- 10. Scott Nollet, Subextremal curves, Manuscripta Math. 94 (1997), no. 3, 303–317. MR 1485438, https://doi.org/10.1007/BF02677855
- 11. Scott Nollet and Enrico Schlesinger, Hilbert schemes of degree four curves, Compositio Math. 139 (2003), no. 2, 169–196. MR 2025805, https://doi.org/10.1023/B:COMP.0000005083.20724.cb
- 12. E. Schlesinger : The spectrum of projective curves, Ph.D. thesis, University of California at Berkeley (1996)
- 13. Yumiko Umezu, Quartic surfaces of elliptic ruled type, Trans. Amer. Math. Soc. 283 (1984), no. 1, 127–143. MR 735411, https://doi.org/10.1090/S0002-9947-1984-0735411-3
- 14. Tohsuke Urabe, Classification of nonnormal quartic surfaces, Tokyo J. Math. 9 (1986), no. 2, 265–295. MR 875189, https://doi.org/10.3836/tjm/1270150719
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14J17, 14N15
Retrieve articles in all journals with MSC (2000): 14J17, 14N15
Additional Information
Sébastien Guffroy
Affiliation:
Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso, 35. 16146 Genova, Italia
Email:
guffroy@math.univ-lille1.fr
DOI:
https://doi.org/10.1090/S0002-9939-07-08966-6
Received by editor(s):
June 1, 2005
Received by editor(s) in revised form:
August 23, 2006
Published electronically:
July 27, 2007
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2007
American Mathematical Society