## Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type

### Summary

Summary: $\noindent$For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than $19$. In this paper we obtain the first results in this direction. In particular the modular variety defined by the orthogonal group of the even unimodular lattice of signature $(2,8m+2)$ is of general type if $m\ge 5$.

14J15, 11F55

### Keywords/Phrases

locally symmetric variety, modular form, Hirzebruch-Mumford proportionality