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Canonical vector heights on K3 surfaces with Picard number three-- An argument for nonexistence

Author: Arthur Baragar
Journal: Math. Comp. 73 (2004), 2019-2025
MSC (2000): Primary 14G40, 11G50, 14J28.
Published electronically: May 7, 2004
MathSciNet review: 2059748
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we investigate a K3 surface with Picard number three and present evidence that strongly suggests a canonical vector height cannot exist on this surface.

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

  • [Ba1] A. Baragar, Canonical vector heights on algebraic K3 surfaces with Picard number two, Canad. Math. Bull., 46 (2003) 495-508.
  • [Ba2] A. Baragar, 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
  • [Bi] H. Billard, Propriétés arithmétiques d'une famille de surfaces K3, Compositio Math. (3) 108 (1997), 247-275. MR 99g:14029
  • [C-S] G. S. Call, J. H. Silverman, Computing the canonical height on K3 surfaces, Math. Comp. (213) 65 (1996), 259-290.MR 96g:11067
  • [S] J. H. Silverman, Rational points on K3 surfaces: A new canonical height, Invent. Math. 105 (1991), 347-373.MR 92k:14025
  • [Wa] L. Wang, 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
  • [Wh] J. Wheler, K3-surfaces with Picard number $2$, Arch. Math. (Basel), (1) 50 (1988), 73-82. MR 89b:14054

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Additional Information

Arthur Baragar
Affiliation: Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada 89154-4020

Keywords: K3 surfaces, canonical vector heights
Received by editor(s): February 14, 2003
Published electronically: May 7, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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