Ekedahl-Oort types of stable curves
Algebraic Geometry
2026-01-26 v3 Number Theory
Abstract
We extend Moonen's definition of Ekedahl-Oort types of smooth curves in terms of Hasse-Witt triples to all stable curves and show that it matches Ekedahl and van der Geer's definition of Ekedahl-Oort types of their generalized Jacobians as semi-abelian varieties. Using this intrinsic insight, we can compute the dimensions of certain Ekedahl-Oort loci of curves and generalize some previously known results about the dimensions of the -rank and -number loci of curves.
Keywords
Cite
@article{arxiv.2307.13445,
title = {Ekedahl-Oort types of stable curves},
author = {Dušan Dragutinović},
journal= {arXiv preprint arXiv:2307.13445},
year = {2026}
}
Comments
Major revisions concerning the presentation of the material. Accepted for publication in the International Journal of Number Theory after minor modifications