Geodesic
The Ample Cone for a K3 Surface
Canadian journal of mathematics, Tome 63 (2011) no. 3, pp. 481-499

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DOI

In this paper, we give several pictorial fractal representations of the ample or Kähler cone for surfaces in a certain class of $K3$ surfaces. The class includes surfaces described by smooth (2, 2, 2) forms in ${{\mathbb{P}}^{1}}\,\times \,{{\mathbb{P}}^{1}}\,\times \,{{\mathbb{P}}^{1}}$ defined over a sufficiently large number field $K$ that have a line parallel to one of the axes and have Picard number four. We relate the Hausdorff dimension of this fractal to the asymptotic growth of orbits of curves under the action of the surface's group of automorphisms. We experimentally estimate the Hausdorff dimension of the fractal to be 1.296 ± .010.
DOI : 10.4153/CJM-2011-006-7
Mots-clés : 14J28, 14J50, 11D41, 11D72, 11H56, 11G10, 37F35, 37D05, Fractal, Hausdorff dimension, K3 surface, Kleinian groups, dynamics 
Baragar, Arthur. The Ample Cone for a K3 Surface. Canadian journal of mathematics, Tome 63 (2011) no. 3, pp. 481-499. doi: 10.4153/CJM-2011-006-7
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     title = {The {Ample} {Cone} for a {K3} {Surface}},
     journal = {Canadian journal of mathematics},
     pages = {481--499},
     year = {2011},
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