English

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 αp\alpha_p-actions. In particular, we obtain non-S3S_3 terminal singularities, as well as locally stable (respectively stable) families whose general fibers are smooth (respectively klt, Cohen--Macaulay and FF-injective) and whose special fibers are non-S2S_2. 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

R2 v1 2026-06-28T20:54:29.239Z