Log-Conformal Projective Manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913041155620864 |
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| author | Corrêa, Maurício Massarenti, Alex |
| author_facet | Corrêa, Maurício Massarenti, Alex |
| contents | Let $(X,Δ)$ be a smooth complex projective simple normal crossing pair of dimension $n\geq 3$ endowed with an everywhere nondegenerate logarithmic conformal tensor. If $K_X+Δ$ is not nef, then precisely one of the following mutually exclusive alternatives occurs: either $Δ=\varnothing$ and $X\simeq Q^n$; or $X\simeq \mathbb{P}^n$ and $Δ$ is a hyperplane; or $n=2m$ is even and $(X,Δ)$ admits a rational maximal isotropic fibration whose geometric generic fibre is the log pair $(\mathbb{P}^m,H)$. If $K_X+Δ\equiv 0$, then, under a Bochner extension principle and an irreducibility assumption on the restricted holonomy of a complete Ricci-flat Kähler metric on $M:=X\setminus Δ$, the existence of a logarithmic conformal tensor with trivial conformal line bundle forces $M$ to be semi-abelian and $(X,Δ)$ to be its toroidal compactification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16215 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-Conformal Projective Manifolds Corrêa, Maurício Massarenti, Alex Algebraic Geometry Differential Geometry Let $(X,Δ)$ be a smooth complex projective simple normal crossing pair of dimension $n\geq 3$ endowed with an everywhere nondegenerate logarithmic conformal tensor. If $K_X+Δ$ is not nef, then precisely one of the following mutually exclusive alternatives occurs: either $Δ=\varnothing$ and $X\simeq Q^n$; or $X\simeq \mathbb{P}^n$ and $Δ$ is a hyperplane; or $n=2m$ is even and $(X,Δ)$ admits a rational maximal isotropic fibration whose geometric generic fibre is the log pair $(\mathbb{P}^m,H)$. If $K_X+Δ\equiv 0$, then, under a Bochner extension principle and an irreducibility assumption on the restricted holonomy of a complete Ricci-flat Kähler metric on $M:=X\setminus Δ$, the existence of a logarithmic conformal tensor with trivial conformal line bundle forces $M$ to be semi-abelian and $(X,Δ)$ to be its toroidal compactification. |
| title | Log-Conformal Projective Manifolds |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2604.16215 |