On the geometry of spaces of filtrations on local rings
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911574711599104 |
|---|---|
| author | Qi, Lu |
| author_facet | Qi, Lu |
| contents | We study the geometry of spaces of fitrations on a Noetherian local domain. We introduce a metric $d_1$ on the space of saturated filtrations, inspired by the Darvas metric in complex geometry, such that it is a geodesic metric space. In the toric case, using Newton-Okounkov bodies, we identify the space of saturated monomial filtrations with a subspace of $L^1_\mathrm{loc}$. We also consider several other topologies on such spaces and study the semi-continuity of the log canonical threshold function in the spirit of Kollár-Demailly. Moreover, there is a natural lattice structure on the space of saturated filtrations, which is a generalization of the classical result that the ideals of a ring form a lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the geometry of spaces of filtrations on local rings Qi, Lu Algebraic Geometry Commutative Algebra Rings and Algebras We study the geometry of spaces of fitrations on a Noetherian local domain. We introduce a metric $d_1$ on the space of saturated filtrations, inspired by the Darvas metric in complex geometry, such that it is a geodesic metric space. In the toric case, using Newton-Okounkov bodies, we identify the space of saturated monomial filtrations with a subspace of $L^1_\mathrm{loc}$. We also consider several other topologies on such spaces and study the semi-continuity of the log canonical threshold function in the spirit of Kollár-Demailly. Moreover, there is a natural lattice structure on the space of saturated filtrations, which is a generalization of the classical result that the ideals of a ring form a lattice. |
| title | On the geometry of spaces of filtrations on local rings |
| topic | Algebraic Geometry Commutative Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2409.01705 |