On the relative Minimal Model Program for threefolds in low characteristics

TL;DR

This paper proves the relative minimal model program for threefolds in all positive characteristics and extends several recent results to low characteristic cases, enhancing the understanding of singularities and divisorial centers.

Contribution

It establishes the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0 and generalizes key results like $W ext{O}$-rationality and inversion of adjunction to low characteristics.

Findings

Validates the relative dlt MMP in all characteristics p>0.

Generalizes $W ext{O}$-rationality of klt singularities to low characteristics.

Shows normality of divisorial centers up to a universal homeomorphism.

Abstract

We show the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0. As a corollary, we generalise many recent results to low characteristics including: $W\mathcal{O}$-rationality of klt singularities, inversion of adjunction, and normality of divisorial centres up to a universal homeomorphism.