Papers › The Kodaira dimension of Hilbert modular threefolds
The Kodaira dimension of Hilbert modular threefolds
Adam Logan
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Following a method introduced by Thomas-Vasquez and developed by Grundman, we prove that many Hilbert modular threefolds of arithmetic genus $0$ and $1$ are of general type, and that some are of nonnegative Kodaira dimension. The new ingredient is a detailed study of the geometry and combinatorics of totally positive integral elements x of a fractional ideal I in a totally real number field K with the property that tr xy < min I tr y for some y ≫0 ∈K.
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