Hirzebruch-Mumford Proportionality and Locally Symmetric Varieties of Orthogonal Type

\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 $m\ge 5$.

2000 Mathematics Subject Classification: 14J15, 11F55

Keywords and Phrases: Locally symmetric variety; modular form; Hirzebruch-Mumford proportionality

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