On the behavior of adjoint ideals under pure morphisms
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918026024058880 |
|---|---|
| author | Takagi, Shunsuke Yamaguchi, Tatsuki |
| author_facet | Takagi, Shunsuke Yamaguchi, Tatsuki |
| contents | We characterize adjoint ideal sheaves via ultraproducts and, utilizing this characterization, study their behavior under pure morphisms. In particular, given a pure morphism $f:Y \to X$ between normal quasi-projective complex varieties, a reduced divisor $D$ and an effective $\mathbb{Q}$-Weil divisor $Γ$ on $X$ without common components, we have the following result: if the cycle-theoretic pullback $E:=f^{\natural}D$ is reduced and $(Y, E+f^*Γ)$ is of plt type along $E$, then $(X, D+Γ)$ is of plt type along $D$. This provides an affirmative answer to a question posed by Z. Zhuang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17537 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the behavior of adjoint ideals under pure morphisms Takagi, Shunsuke Yamaguchi, Tatsuki Algebraic Geometry Commutative Algebra 03C20, 13A35, 14B05, 14F18, 14J17 We characterize adjoint ideal sheaves via ultraproducts and, utilizing this characterization, study their behavior under pure morphisms. In particular, given a pure morphism $f:Y \to X$ between normal quasi-projective complex varieties, a reduced divisor $D$ and an effective $\mathbb{Q}$-Weil divisor $Γ$ on $X$ without common components, we have the following result: if the cycle-theoretic pullback $E:=f^{\natural}D$ is reduced and $(Y, E+f^*Γ)$ is of plt type along $E$, then $(X, D+Γ)$ is of plt type along $D$. This provides an affirmative answer to a question posed by Z. Zhuang. |
| title | On the behavior of adjoint ideals under pure morphisms |
| topic | Algebraic Geometry Commutative Algebra 03C20, 13A35, 14B05, 14F18, 14J17 |
| url | https://arxiv.org/abs/2312.17537 |