The Kodaira dimension of Hilbert modular threefolds
Abstract
Following a method introduced by Thomas-Vasquez and developed by Grundman, we prove that many Hilbert modular threefolds of geometric genus 0 0 and 1 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 x of a fractional ideal I I in a totally real number field K K with the property that tr x y > min I tr y \operatorname {tr} xy > \min I \operatorname {tr} y for some y ≫ 0 ∈ K y \gg 0 \in K .
Fields of Study & Subjects
Advanced Algebra and Geometry
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 229–259
- Publication date
- 1 May 2026
- Language
- EN