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math.AG2025
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…
math.AG2025
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…
math.AG2023
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 \…