arXiv subjects

Marta Benozzo

Publications and source records attributed to Marta Benozzo.

5 recordsLinked to original sources

arXiv2026

Base-change of locally stable families in positive characteristic

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 on previous work of Hu--Zong, we show that it suffices to consider base-changes by Frobenius morphisms. In that case, we show that the situation is governed by the discrepancies of the pairs $(X,X_c)$, together with some differential invariants of the vertical divisors whose multiplicity in their fiber is divisible by $p$. While the behaviour of these invariants remains in general mysterious, we establish upper bounds under some $F$-splitting assumptions.

math.AG↗

arXiv2025

Bounds on the plus-pure thresholds of some hypersurfaces in (ramified) regular rings

We study the plus-pure threshold (ppt) of hypersurfaces in mixed characteristic. We show that the ppt limits to the $F$-pure threshold (fpt) as we ramify the base DVR. Additionally, we show that analogs of some positive characteristic extremal singularities cannot attain the same `extremal' ppt values in the unramified setting. We also study equations which have controlled ramification when we adjoin their $p$-th roots as well as equations which admit $p$-th roots modulo $p^2$ (or modulo other values), bounding their ppts. In particular, given a complete unramified regular local ring of mixed characteristic $p>0$, $f^p + p^2 g$ does not define a perfectoid pure singularity for any $f$ and $g$. Finally, we compute bounds on the ppt of hypersurfaces related to elliptic curves. This gives examples where the ppt is neither the corresponding fpt in characteristic $p > 0$ nor the lct in characteristic zero. This also provides examples where $p$ times the ppt is not a jumping number, in stark contrast with the characteristic $p > 0$ picture.

math.AC↗

arXiv2023

On the superadditivity of anticanonical Iitaka dimension

Given a fibration $f: X \to Y$ with normal general fibre $X_y$, over a field of any characteristic, we establish the Iitaka-type inequality $\kappa(X,-K_X) \leq \kappa(X_y,-K_{X_y})+\kappa(Y,-K_Y)$ whenever the $\mathbb{Q}$-linear series $|-K_X|_{\mathbb{Q}}$ has good singularities on $X_y$.

math.AG↗

arXiv2023

On the canonical bundle formula in positive characteristic

Let $f: X \to Z$ be a fibration from a normal projective variety $X$ of dimension $n$ onto a normal curve $Z$ over a perfect field of characteristic $p>2$. Let $(X, B)$ be a dlt pair such that the induced pair on a general fibre is log canonical. Assuming the LMMP and the existence of log resolutions in dimension $\leq n$, we prove that, when $K_X+B$ is $f$-nef, the moduli part is nef up to a birational map $Y \dashrightarrow X$. As a corollary, we prove positivity of the moduli part in the $K$-trivial case, i.e. when $K_X+B \sim_{\Q} f^*L$ for some $\Q$-Cartier $\Q$-divisor $L$ on $Z$. In particular, consider a dlt pair $(X, B)$ of dimension $3$ over an algebraically closed field of characteristic $p>5$ such that the induced pair on a general fibre is log canonical, then the canonical bundle formula holds unconditionally.

math.AG↗

arXiv2022

On the Iitaka conjecture for anticanonical divisors in positive characteristic

Given a fibration over a perfect field of positive characteristic, we study an Iitaka-type inequality for the anticanonical divisors. We conclude that it holds when the source of the fibration is a threefold or when the target is a curve, the general fibre is regular and the pair induced on it from the ambient space is strongly F-regular. We then give counterexamples in characteristics 2 and 3 for fibrations with non-normal fibres, constructed from Tango--Raynaud surfaces.

math.AG↗