Tatsuro Kawakami

activity

20232026

collaborators

6 papers

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

Inversion of adjunction for higher rational singularities

Tatsuro Kawakami, Jakub Witaszek

We prove inversion of adjunction for higher rational singularities.

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 Rösler

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

math.AG2023

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…