Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Three-divisible families of skew lines on a smooth projective quintic

Author: Slawomir Rams
Journal: Trans. Amer. Math. Soc. 354 (2002), 2359-2367
MSC (2000): Primary 14M99; Secondary 14E20.
Published electronically: February 7, 2002
MathSciNet review: 1885656
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give an example of a family of 15 skew lines on a quintic such that its class is divisible by 3. We study properties of the codes given by arrangements of disjoint lines on quintics.

References [Enhancements On Off] (What's this?)

  • 1. W. Barth: Even sets of eight skew lines on a K3 surface, preprint.
  • 2. W. Barth, I. Nieto: Abelian surfaces of type (1,3) and quartic surfaces with 16 skew lines. J. Alg. Geom. 3 (1994) , 173-222. MR 95e:14033
  • 3. W. Barth, A. Peters, A. Van de Ven: Compact Complex Surfaces. Berlin, Heidelberg, New York: Springer, 1984. MR 86c:32026
  • 4. A. Beauville: Sur le nombre maximum de points doubles d'une surface dans $\mathbb{P}^3$ ( $\mu( 5 ) = 31$). in Journées de géometrie algebrique d'Angers (1979), Sijthoff-Noordhoff, 1980, pp. 207-215. MR 82k:14037
  • 5. L. Caporaso, J. Harris, B. Mazur: How many rational points can a curve have? in The Moduli Space of Curves (R. Dijkgraaf, C Faber, G. van der Geer eds.), Progress in Math. 129, Birkhäuser Verlag, 1995, pp. 13-31. MR 97d:11099
  • 6. P. Griffiths , J. Harris: Principles of algebraic geometry. New York, Chichester, Brisbane, Toronto, Singapore, John Wiley and Sons, Inc., 1978. MR 80b:14001
  • 7. Sheng-Li Tan: Cusps on some algebraic surfaces, preprint, 1999.
  • 8. R. Miranda: On triple covers in algebraic geometry Amer. J. Math. 107 (1985), 1123-1158. MR 86k:14008
  • 9. Y. Miyaoka: The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants, Math. Ann. 268 (1984) , 159-171. MR 85j:14060
  • 10. V.V. Nikulin: On Kummer Surfaces, Math. USSR. Izv. 9 (1975), no. 2, 261-275. MR 55:2926
  • 11. J.H. van Lint: Introduction to Coding Theory. Berlin: Springer, 1992. MR 94b:94001
  • 12. D. van Straten: Macaulay script to estimate the number of lines on a surface with some examples of surfaces.
  • 13. B. Segre: The maximum number of lines lying on a quartic surface, Quart. J. Math. Oxford Ser. 14 (1943), 86-96. MR 6:16g

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14M99, 14E20.

Retrieve articles in all journals with MSC (2000): 14M99, 14E20.

Additional Information

Slawomir Rams
Affiliation: Institute of Mathematics, Jagiellon University, Reymonta 4, PL-30-059 Kraków, Poland
Address at time of publication: Mathematisches Institut, FAU Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054 Erlangen, Germany
Email: and

Keywords: Quintic, cyclic cover, code.
Received by editor(s): December 31, 2000
Published electronically: February 7, 2002
Additional Notes: This research was supported by DFG contract BA 423/8-1
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society