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Orbits of points on certain K3 surfaces

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Volume
131
Issue
3
Identifiers
DOI: 10.1016/j.jnt.2010.09.012
Keywords
  • K3 Surface
  • Orbits
  • Automorphism
  • Hausdorff Dimension
  • Ample Cone
Disciplines
  • Mathematics

Abstract

Abstract In this paper we show that, for a K3 surface within a certain class of surfaces and over a number field, the orbit of a point under the group of automorphisms is either finite or its exponent of growth is exactly the Hausdorff dimension of a fractal associated to the ample cone. In particular, the exponent depends on the geometry of the surface and not its arithmetic. For surfaces in this class, the exponent is 0.6527±0.0012.

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