2025/01/27 by Logan, Adam
#11F41 #11Y40 #14G35 #14J30 (Primary) #32S45 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2501.15719
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 \mathoptr xy < \mathopmin I \mathoptr y for some y ≫ 0 ∈ K.