  In this paper, we apply the Bestvina-Mess type formula for relatively
hyperbolic groups, which is established by Tomohiro Fukaya, to automorphism
groups of K3 surfaces, and we show that the virtual cohomological dimension of
automorphism groups of K3 surfaces determined by the covering dimension of the
blown-up boundaries associated with their ample cones.

Algebraic Geometry;Group Theory