On the birational automorphisms of varieties of general type


We show that the number of birational automorphisms of a variety of general type $X$ is bounded by $c \cdot \mathrm{vol}(X,K_X)$, where $c$ is a constant that only depends on the dimension of $X$.


Christopher D. Hacon

Department of Mathematics, The University of Utah, 155 S 1400 E, Salt Lake City, UT 84112-0090

James M$^{\textbf{c}}$Kernan

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139-4307

Chenyang Xu

Beijing International Center of Mathematics Research, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, China P.R.