Functorial monomialization and uniqueness of centers for relative principalization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929762283290624 |
|---|---|
| author | Abramovich, Dan Temkin, Michael Włodarczyk, Jarosław |
| author_facet | Abramovich, Dan Temkin, Michael Włodarczyk, Jarosław |
| contents | Theorem 1.2.6 of [ATW20] provides a relatively functorial logarithmic principalization of ideals on relative logarithmic orbifolds $X\to B$ in characteristic 0, relying on a delicate monomialization theorem for Kummer ideals. The paper [AdSTW25] provides a parallel avenue through weighted blowings up. In this paper we show that, if $X\to B$ is proper, monomialization of both Kummer and weighted logarithmic centers can be carried out in a manner which is functorial for base change by regular morphisms. This implies in particular logarithmic relative principalization of ideals and logarithmically smooth reduction of proper families of varieties in characteristic 0 in a manner equivariant for group actions and compatible with localization on the base. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functorial monomialization and uniqueness of centers for relative principalization Abramovich, Dan Temkin, Michael Włodarczyk, Jarosław Algebraic Geometry 14E15, 14A20, 14A21 Theorem 1.2.6 of [ATW20] provides a relatively functorial logarithmic principalization of ideals on relative logarithmic orbifolds $X\to B$ in characteristic 0, relying on a delicate monomialization theorem for Kummer ideals. The paper [AdSTW25] provides a parallel avenue through weighted blowings up. In this paper we show that, if $X\to B$ is proper, monomialization of both Kummer and weighted logarithmic centers can be carried out in a manner which is functorial for base change by regular morphisms. This implies in particular logarithmic relative principalization of ideals and logarithmically smooth reduction of proper families of varieties in characteristic 0 in a manner equivariant for group actions and compatible with localization on the base. |
| title | Functorial monomialization and uniqueness of centers for relative principalization |
| topic | Algebraic Geometry 14E15, 14A20, 14A21 |
| url | https://arxiv.org/abs/2503.13345 |