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math.AG2026

Quasi--splitting versus log canonicity

Kenta Sato, Shunsuke Takagi, Shou Yoshikawa

In this paper, we investigate the relationship between quasi--splitting and log canonicity. We show that if a numerically -Gorenstein normal singularity is quasi-$F^…

math.AG2026

Quasi--singularities and singularities in birational geometry

Tatsuro Kawakami, Shunsuke Takagi, Shou Yoshikawa

We give an overview of the theory of quasi--singularities, focusing on their connection with singularities in birational geometry.

math.AG2026

An explicit formula for the Artin invariant of smooth K3 hypersurfaces

Teppei Takamatsu, Shou Yoshikawa

We characterize the Artin invariant of a smooth K3 hypersurface in terms of quasi--splitting. As an application, we obtain an explicit formula for this invariant.

math.AG2026

Perfectoid pure thresholds of lifts of rational double points

Teppei Takamatsu, Shou Yoshikawa

We study the perfectoid pure threshold with respect to , an invariant of singularities in mixed characteristic arising from perfectoid purity. In this paper, we compute…

math.AG2026

Non-quasi--split canonical affine fourfolds exist in every characteristic

Teppei Takamatsu, Shou Yoshikawa

We construct canonical -factorial Gorenstein affine fourfolds in every positive characteristic that are not quasi--split.

math.AC2026

Quasi--split height versus quasi--regular height for rational double points and graded rings

Teppei Takamatsu, Shou Yoshikawa

In this paper, we study a phenomenon concerning quasi--singularities: under suitable hypotheses, the finiteness of the quasi--split height () i…