Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Rational curves on K3 surfaces in $\mathbb P^1\times \mathbb P^1 \times \mathbb P^1$


Author: Arthur Baragar
Journal: Proc. Amer. Math. Soc. 126 (1998), 637-644
MSC (1991): Primary 14J28, 14J50, 14G05
DOI: https://doi.org/10.1090/S0002-9939-98-04427-X
MathSciNet review: 1459107
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss Manin and Batyrev's notion of the arithmetic stratification of a variety, and, for an irreducible surface $V$ embedded in $\mathbb P^m$, compare it with the spectrum of degrees of rational curves on $V$. We study this spectrum for the class of K3 surfaces generated by smooth (2,2,2) forms in $\mathbb P^1\times \mathbb P^1 \times \mathbb P^1$.


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

  • [B] Baragar, A., Rational points on K3 surfaces in ${\mathbb P}^1\times {\mathbb P}^1 \times {\mathbb P}^1$, Math. Ann. 305 (1996), 541-558. MR 97g:14020
  • [B-M] Batyrev, V. V., Manin, Yu. I., Sur le nombre des points rationnels de hauteur borné des variétés algébriques, Math. Ann. 286 (1990), 27 - 43. MR 91g:11069
  • [F-M-T] Franke, J., Manin, Yu. I., Tschinkel, Yu., Rational Points of Bounded Height on Fano Varieties, Invent. Math. 95 (1989), 421 - 435; 102 (1990), 463. MR 89m:11060; MR 91i:11068
  • [L] Lang, S., Number Theory III, New York: Springer Verlag 1991. MR 93a:11048
  • [S] Silverman, J. H., Rational Points on K3 Surfaces: A New Canonical Height, Invent. Math. 105 (1991), 347 - 373. MR 92k:14025
  • [T] Tschinkel, Yu., Finite Heights and Rational Points on Surfaces, Advances in Number Theory, F. Gouvea and N. Yui (eds.), Oxford University Press 1991, 319 - 329. MR 97a:11100
  • [V-W] Vaughan, R. C., Wooley, T. D., On a certain nonary cubic form and related equations, Duke Math. J. 80 (1995), 669 - 735. MR 96j:11038
  • [W1] Wang, L., Rational Points and Canonical Heights on K3-surfaces in ${\mathbb P}^1\times {\mathbb P}^1 \times {\mathbb P}^1$, Contemporary Math. 186 (1995), 273 - 289. MR 97a:14023
  • [W2] -, The Automorphism Groups of K3 Surfaces with Picard Number 3, (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14J28, 14J50, 14G05

Retrieve articles in all journals with MSC (1991): 14J28, 14J50, 14G05


Additional Information

Arthur Baragar
Affiliation: Department of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Address at time of publication: Department of Mathematical Sciences, University of Nevada, Las Vegas, Nevada 89154-4020
Email: baragar@nevada.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04427-X
Received by editor(s): May 9, 1996
Communicated by: Ron Donagi
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society