Abstract
We realize the Apollonian group associated to an integral Apollonian circle packings, and some of its generalizations, as a group of automorphisms of an algebraic surface. Borrowing some results in the theory of orbit counting, we study the asymptotic of the growth of degrees of elements in the orbit of a curve on an algebraic surface with respect to a geometrically finite group of its automorphisms.
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To the memory of Andrey Todorov
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© 2016 Springer International Publishing Switzerland
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Dolgachev, I. (2016). Orbital Counting of Curves on Algebraic Surfaces and Sphere Packings. In: Faber, C., Farkas, G., van der Geer, G. (eds) K3 Surfaces and Their Moduli. Progress in Mathematics, vol 315. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29959-4_2
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DOI: https://doi.org/10.1007/978-3-319-29959-4_2
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-29958-7
Online ISBN: 978-3-319-29959-4
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