Log canonical thresholds at infinity
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917262372372480 |
|---|---|
| author | Bivià-Ausina, Carles Rashkovskii, Alexander |
| author_facet | Bivià-Ausina, Carles Rashkovskii, Alexander |
| contents | The paper considers a global version of the notion of log canonical threshold for plurisubharmonic functions $u$ of logarithmic growth in $\mathbb{C}^n$, aiming at description of the range of all $p>0$ such that $e^{-u}\in L^p(\mathbb{C}^n)$. Explicit formulas are obtained in the toric case. By considering Bergman functions of corresponding weighted Hilbert spaces, a new polynomial approximation of plurisubharmonic functions of logarithmic growth with control over its singularities and behavior at infinity (a global version of Demailly's approximation theorem) is established. Some application to tame polynomial maps are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log canonical thresholds at infinity Bivià-Ausina, Carles Rashkovskii, Alexander Complex Variables The paper considers a global version of the notion of log canonical threshold for plurisubharmonic functions $u$ of logarithmic growth in $\mathbb{C}^n$, aiming at description of the range of all $p>0$ such that $e^{-u}\in L^p(\mathbb{C}^n)$. Explicit formulas are obtained in the toric case. By considering Bergman functions of corresponding weighted Hilbert spaces, a new polynomial approximation of plurisubharmonic functions of logarithmic growth with control over its singularities and behavior at infinity (a global version of Demailly's approximation theorem) is established. Some application to tame polynomial maps are given. |
| title | Log canonical thresholds at infinity |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2601.23118 |