5 papers
BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic
Tatsuki Yamaguchi
We introduce a new method for computing plus-pure thresholds, a mixed-characteristic analogue of both log canonical thresholds and -pure thresholds. We obtain some necessary con…
On the uniform positivity of -signature under reduction modulo
Shunsuke Takagi, Tatsuki Yamaguchi
Carvajal-Rojas, Schwede and Tucker asked whether the mod reductions of a complex klt type singularity have uniformly positive -signature for almost all primes . In this p…
Ultra-test ideals in rings with finitely generated anti-canonical algebras
Tatsuki Yamaguchi
When anti-canonical rings are finitely generated, we give a characterization of adjoint ideals using ultra-Frobenii, a characteristic zero analogue of Frobenius morphisms. This cha…
-pure and -injective singularities in equal characteristic zero
Tatsuki Yamaguchi
Inspired by Schoutens' results, we introduce a variant of sharp -purity and sharp -injectivity in equal characteristic zero via ultraproducts. As an application, we show that…
On the behavior of adjoint ideals under pure morphisms
Shunsuke Takagi, Tatsuki Yamaguchi
We characterize adjoint ideal sheaves via ultraproducts and, utilizing this characterization, study their behavior under pure morphisms. In particular, given a pure morphism $f:Y \…