Pathology of formal locally-trivial deformations in positive characteristic

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 $(H_1)$ in [3], in contrast to the complex/characteristic $0$ case. The first example is an algebraic curve, and the second is a normal rational projective surface with only one rational double point.

17pages. A new version of the proof of Theorem 1.1 for curves is on arXiv:2509.00887v2