Partial Hasse invariants for genus zero curves in Hilbert modular varieties
Number Theory
2026-01-26 v1 Algebraic Geometry
Abstract
We construct characteristic-zero lifts of partial Hasse invariants for genus zero non-compact curves in Hilbert modular varieties. The construction is based on recent results on the associated Picard-Fuchs differential equations. As an application, we relate the size of the non-ordinary locus of the modulo reduction of these curves to the dimension of spaces of (twisted) modular forms. We compute it explicitly for several Teichm\"uller curves, obtaining Deuring-like formulae. Moreover, we study the modulo reduction of (twisted) modular forms on not necessarily arithmetic genus-zero Fuchsian groups with modular embedding.
Cite
@article{arxiv.2601.16929,
title = {Partial Hasse invariants for genus zero curves in Hilbert modular varieties},
author = {Gabriele Bogo and Yingkun Li},
journal= {arXiv preprint arXiv:2601.16929},
year = {2026}
}