Pathological MMP singularities as $\alpha_p$-quotients
Algebraic Geometry
2025-08-12 v2
Abstract
We construct pathological examples of MMP singularities in every positive characteristic using quotients by -actions. In particular, we obtain non- terminal singularities, as well as locally stable (respectively stable) families whose general fibers are smooth (respectively klt, Cohen--Macaulay and -injective) and whose special fibers are non-. The dimensions of these examples are bounded below by a linear function of the characteristic.
Keywords
Cite
@article{arxiv.2501.01179,
title = {Pathological MMP singularities as $\alpha_p$-quotients},
author = {Quentin Posva},
journal= {arXiv preprint arXiv:2501.01179},
year = {2025}
}
Comments
v2: 27 pages, comments welcome anytime. Some results have been improved, some minor mistakes have been corrected