Quentin Posva

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math.AG2026

Local stability of Frobenius and Artin--Schreier base-change: a comparison

Quentin Posva

Let $(X, Δ) \to C$ be a family of pairs over a smooth curve in positive characteristic $p > 0$ . We study the discrepancies of divisors over the base-change $(X, Δ) \to C$ along Artin--Sc…

math.AG2026

Base-change of locally stable families in positive characteristic

Marta Benozzo, Quentin Posva

We investigate the permanence of local stability for one-parameter families $X \to C$ under finite flat base-changes, when the base-field has positive characteristic $p > 0$ . Building…

math.AG2026

On linear $α_{p}$ -quotients

Quentin Posva, Linus Rösler, Takehiko Yasuda

We study linear $α_{p}$ -actions on affine spaces and the associated quotient singularities, using explicit stacky resolutions. We describe when the quotient singularities are log can…

math.AG2025

Pathological MMP singularities as $α_{p}$ -quotients

Quentin Posva

We construct pathological examples of MMP singularities in every positive characteristic using quotients by $α_{p}$ -actions. In particular, we obtain non- $S_{3}$ terminal singularities…

Local stability of Frobenius and Artin--Schreier base-change: a comparison

Base-change of locally stable families in positive characteristic

On linear αp​-quotients

Pathological MMP singularities as αp​-quotients

On linear $α_{p}$ -quotients

Pathological MMP singularities as $α_{p}$ -quotients