Pathology of formal locally-trivial deformations in positive characteristic
Algebraic Geometry
2025-12-16 v2
Abstract
We construct explicit examples that are algebraic varieties in positive characteristic to show that locally trivial moduli functors do not always satisfy Schlessinger's condition in [3], in contrast to the complex/characteristic case. The first example is an algebraic curve, and the second is a normal rational projective surface with only one rational double point.
Keywords
Cite
@article{arxiv.2502.00332,
title = {Pathology of formal locally-trivial deformations in positive characteristic},
author = {Takuya Miyamoto},
journal= {arXiv preprint arXiv:2502.00332},
year = {2025}
}
Comments
17pages. A new version of the proof of Theorem 1.1 for curves is on arXiv:2509.00887v2