Orbital counting of curves on algebraic surfaces and sphere packings
Algebraic Geometry
2014-09-03 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1408.0374,
title = {Orbital counting of curves on algebraic surfaces and sphere packings},
author = {Igor Dolgachev},
journal= {arXiv preprint arXiv:1408.0374},
year = {2014}
}
Comments
42 pages, 5 figures. New references have been added that allowed the author to strengthen some of the main results of the paper. Also some minor corrections have been made