Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Three-divisible families of skew lines on a smooth projective quintic
HTML articles powered by AMS MathViewer

by Sławomir Rams PDF
Trans. Amer. Math. Soc. 354 (2002), 2359-2367 Request permission

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
  • W. Barth: Even sets of eight skew lines on a K3 surface, preprint.
  • W. Barth and I. Nieto, Abelian surfaces of type $(1,3)$ and quartic surfaces with $16$ skew lines, J. Algebraic Geom. 3 (1994), no. 2, 173–222. MR 1257320
  • W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574, DOI 10.1007/978-3-642-96754-2
  • Arnaud Beauville, Sur le nombre maximum de points doubles d’une surface dans $\textbf {P}^{3}$ $(\mu (5)=31)$, Journées de Géometrie Algébrique d’Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den Rijn—Germantown, Md., 1980, pp. 207–215 (French). MR 605342
  • Lucia Caporaso, Joe Harris, and Barry Mazur, How many rational points can a curve have?, The moduli space of curves (Texel Island, 1994) Progr. Math., vol. 129, Birkhäuser Boston, Boston, MA, 1995, pp. 13–31. MR 1363052, DOI 10.1007/978-1-4612-4264-2_{2}
  • Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
  • Sheng-Li Tan: Cusps on some algebraic surfaces, preprint, 1999.
  • Rick Miranda, Triple covers in algebraic geometry, Amer. J. Math. 107 (1985), no. 5, 1123–1158. MR 805807, DOI 10.2307/2374349
  • Yoichi Miyaoka, The maximal number of quotient singularities on surfaces with given numerical invariants, Math. Ann. 268 (1984), no. 2, 159–171. MR 744605, DOI 10.1007/BF01456083
  • V. V. Nikulin, Kummer surfaces, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 2, 278–293, 471 (Russian). MR 0429917
  • J. H. van Lint, Introduction to coding theory, 2nd ed., Graduate Texts in Mathematics, vol. 86, Springer-Verlag, Berlin, 1992. MR 1217490, DOI 10.1007/978-3-662-00174-5
  • D. van Straten: Macaulay script to estimate the number of lines on a surface with some examples of surfaces.
  • Albert Eagle, Series for all the roots of the equation $(z-a)^m=k(z-b)^n$, Amer. Math. Monthly 46 (1939), 425–428. MR 6, DOI 10.2307/2303037
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
  • Sławomir 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: rams@mi.uni-erlangen.de and rams@im.uj.edu.pl
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2359-2367
  • MSC (2000): Primary 14M99; Secondary 14E20
  • DOI: https://doi.org/10.1090/S0002-9947-02-02979-3
  • MathSciNet review: 1885656