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Projective surfaces with many skew lines
Author(s):
Slawomir
Rams
Journal:
Proc. Amer. Math. Soc.
133
(2005),
11-13.
MSC (2000):
Primary 14J25;
Secondary 14J70
Posted:
August 20, 2004
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Abstract:
We give an example of a smooth surface  of degree  that contains  pairwise disjoint lines. In particular, our example shows that the degree in Miyaoka's bound is sharp.
References:
-
- 1.
- 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 1257320 (95e:14033)
- 2.
- T. Bauer: Quartic surfaces with 16 skew conics. J. Reine. Angew. Math. 464 (1995) , 207-217. MR 1340342 (96j:14024)
- 3.
- 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 1363052 (97d:11099)
- 4.
- Y. Miyaoka: The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants, Math. Ann. 268 (1984) , 159-171. MR 0744605 (85j:14060)
- 5.
- S. Rams: Three-divisible families of skew lines on a smooth projective quintic, Trans. Amer. Math. Soc. 354 (2002), 2359-2367. MR 1885656 (2003b:14064)
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Additional Information:
Slawomir
Rams
Affiliation:
Institute of Mathematics UJ, ul. Reymonta 4, 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, rams@im.uj.edu.pl
DOI:
10.1090/S0002-9939-04-07519-7
PII:
S 0002-9939(04)07519-7
Keywords:
Miyaoka's bound,
skew lines
Received by editor(s):
April 6, 2002
Received by editor(s) in revised form:
August 27, 2003
Posted:
August 20, 2004
Additional Notes:
Partially supported by DFG contract BA 423/8-1 and the Foundation for Polish Science.
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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