arXiv subjects

Linus Rösler

Publications and source records attributed to Linus Rösler.

5 recordsLinked to original sources

arXiv2026

On Gorenstein $\mathbb{Q}_p$-rational threefold and fourfold singularities

We prove that for $n \leq 4$ and $p > 5$, quasi--Gorenstein $F$--pure and $\mathbb{Q}_p$--rational $n$--fold singularities are canonical. This is analogous to the usual fact that rational Gorenstein singularities are canonical. The proof is based on a careful analysis of the dual complex of a dlt modification of a log canonical singularity. The result for $n = 4$ is contingent upon the existence of log resolutions.

math.AG↗

arXiv2026

On linear $α_p$-quotients

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 canonical, canonical or terminal, and we compute their stringy motivic invariants. The second author and Fabio Tonini conjectured that these invariants coincide with those of linear $\mathbb{Z}/p$-quotients: our approach reduces this conjecture to an equality of explicit multi-sets, which we check for a large number of primes using a computer software. A general proof of the equality of multi-sets is given in the appendix written by Linus Rösler.

math.AG↗

arXiv2026

On the birational isotriviality of the Albanese morphism of a log Calabi-Yau pair with a torus action

Let $(X,Δ)$ be a projective, log canonical, $K$-trivial pair over the complex numbers. Let $Z$ be a minimal log canonical center of $(X,Δ)$ and suppose that there exists a torus $\mathbb{T}\subseteq\operatorname{Aut}(X)$ preserving $Δ$ and such that $\dim\mathbb{T}=\operatorname{codim}_X Z$. Then we show that two general fibers of the Albanese morphism $\operatorname{alb}_X$ are birationally equivalent. In particular, the pathological example of a projective, log canonical, $K$-trivial variety whose Albanese morphism is not generically birationally isotrivial, recently constructed by Bernasconi, Filipazzi, Patakfalvi and Tsakanikas, can be avoided under the additional hypothesis that there exists a torus of large enough dimension in the automorphism group of the given pair.

math.AG↗

arXiv2026

On Seshadri constants of adjoint divisors on surfaces and threefolds in arbitrary characteristic

We develop a new approach towards obtaining lower bounds of the Seshadri constants of ample adjoint divisors on smooth projective varieties $X$ in arbitrary characteristic. Let $x\in X$ be a closed point and $A$ an ample divisor on $X$. If $X$ is a surface, we recover some known lower bounds by proving, e.g., that $\varepsilon(K_X+4A;x)\geq 3/4$. If $X$ is a threefold, we prove that for all $δ>0$ and all but finitely many curves $C$ through $x$, we have $\frac{(K_X+6A).C}{\operatorname{mult}_x C}\geq\frac{1}{2\sqrt{2}}-δ$. In particular, if $\varepsilon(K_X+6A;x)<1/(2\sqrt{2})$, then $\varepsilon(K_X+6A;x)$ is a rational number, attained by a Seshadri curve $C$.

math.AG↗

arXiv2025

On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type

Given a Cohen-Macaulay scheme of klt type $X$ and a resolution $π\colon Y\to X$, we show that $R^1π_*ω_Y=0$. We deduce that if $\mathrm{dim}(X)=3$, then $X$ satisfies Grauert-Riemenschneider vanishing and therefore has rational singularities. We also obtain that in arbitrary dimension, if $X$ is of finite type over a perfect field of characteristic $p>0$, then $X$ has $\mathbb{Q}_p$-rational singularities.

math.AG↗