Quasi-F-splittings in birational geometry III

Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko, Shou Yoshikawa

Abstract

We prove that $\mathbb Q$-Gorenstein quasi-$F$-regular singularities are klt. To this end, we shall introduce quasi-test ideals.

We prove that

-Gorenstein quasi-

-regular singularities are klt. To this end, we shall introduce quasi-test ideals.

Paper Structure (34 sections, 103 theorems, 458 equations, 1 figure)

This paper contains 34 sections, 103 theorems, 458 equations, 1 figure.

Theorem A

Let $R$ be an $F$-finite normal Noetherian $\mathbb{Q}$-Gorenstein domain over $\mathbb{F}_p$. If $R$ is quasi-$F$-regular, then it is klt.

Figure 1: Relation between singularities when $R$ is $\mathbb{Q}$-Gorenstein.

Theorem A: Theorem \ref{['thm:qFR to klt pair']}
Theorem B: Theorem \ref{['t-3-dim-klt']}
Theorem C: Theorem \ref{['thm:QFR for klt']}
Theorem D
Definition 1.1
Remark 1.2
Theorem E: Theorem \ref{['thm: rel q+R, qFrat and qFR']}
Theorem F: Theorem \ref{['thm:best-def-quasi-F-regular-Section4']}
Theorem G: Theorem \ref{['thm:qFs to qFr']}, Corollary \ref{['qFs to qFr for am Fano']}
proof : Sketch of the proof
...and 280 more