E8 lattice and the Kodaira dimension of orthogonal modular varieties
arXiv:1306.2129
Abstract
We prove that for any even lattice L of signature (2,n), the modular variety defined by the orthogonal group of the lattice L+mE_8 is of general type when m is sufficiently large.
The previous version contained a serious error in page 12, line 22-23. It is possible to modify the main theorem, but this is now contained in arXiv:1309.7121v3