The Lee--Gauduchon cone on complex manifolds
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914040664555520 |
|---|---|
| author | Ornea, Liviu Verbitsky, Misha |
| author_facet | Ornea, Liviu Verbitsky, Misha |
| contents | Let $M$ be a compact complex $n$-manifold. A Gauduchon metric is a Hermitian metric whose fundamental 2-form $ω$ satisfies the equation $dd^c(ω^{n-1})=0$. Paul Gauduchon has proven that any Hermitian metric is conformally equivalent to a Gauduchon metric, which is unique (up to a constant multiplier) in its conformal class. Then $d^c(ω^{n-1})$ is a closed $(2n-1)$-form; the set of cohomology classes of all such forms, called the Lee-Gauduchon cone, is a convex cone, superficially similar to the Kahler cone. We prove that the Lee-Gauduchon cone is a bimeromorphic invariant, and compute it for several classes of non-Kahler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Lee--Gauduchon cone on complex manifolds Ornea, Liviu Verbitsky, Misha Differential Geometry Complex Variables 53C55, 32H04 Let $M$ be a compact complex $n$-manifold. A Gauduchon metric is a Hermitian metric whose fundamental 2-form $ω$ satisfies the equation $dd^c(ω^{n-1})=0$. Paul Gauduchon has proven that any Hermitian metric is conformally equivalent to a Gauduchon metric, which is unique (up to a constant multiplier) in its conformal class. Then $d^c(ω^{n-1})$ is a closed $(2n-1)$-form; the set of cohomology classes of all such forms, called the Lee-Gauduchon cone, is a convex cone, superficially similar to the Kahler cone. We prove that the Lee-Gauduchon cone is a bimeromorphic invariant, and compute it for several classes of non-Kahler manifolds. |
| title | The Lee--Gauduchon cone on complex manifolds |
| topic | Differential Geometry Complex Variables 53C55, 32H04 |
| url | https://arxiv.org/abs/2411.05595 |