Tatsuro Kawakami

collaborators

6 papers

math.AG2026

The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails

Jefferson Baudin, Fabio Bernasconi, Tatsuro Kawakami

We show that the Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails for threefolds in any positive characteristic, and for terminal 3-folds in charac…

math.AG2026

Inversion of adjunction for higher rational singularities

Tatsuro Kawakami, Jakub Witaszek

We prove inversion of adjunction for higher rational singularities.

math.AG2026

Local vanishing for F-pure threefolds

Tatsuro Kawakami

We establish Grauert--Riemenschneider vanishing for $F$ -pure threefolds over a perfect field $k$ of characteristic $p > 5$ . We apply this to prove Steenbrink vanishing for three-dime…

math.AG2026

Higher F-rational singularities

Tatsuro Kawakami, Jakub Witaszek

We introduce higher $F$ -rationality generalising $F$ -rationality. We prove that a normal variety over a field of characteristic zero is $m$ -rational if and only if it is $m$ - $F$ -ra…

math.AG2025

Frobenius liftable hypersurfaces

Tatsuro Kawakami, Supravat Sarkar, Jakub Witaszek

Let $D$ be a reduced divisor in $P_{k}^{n}$ for an algebraically closed field $k$ of positive characteristic $p > 0$ . We prove that if $(P_{k}^{n}, D)$ is Frobenius liftabl…

math.AG2025

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

Jefferson Baudin, Tatsuro Kawakami, Linus RÃ¶sler

Given a Cohen-Macaulay scheme of klt type $X$ and a resolution $I ¨ : Y \to X$ , we show that $R^{1} I ¨ _{*} I ¨ _{Y} = 0$ . We deduce that if $dim (X) = 3$ , then $X$ satisfies Grauert-Ri…