Singularity of non-pluripolar cohomology classes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913998646018048 |
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| author | Nguyen, Duc-Bao Su, Shuang Vu, Duc-Viet |
| author_facet | Nguyen, Duc-Bao Su, Shuang Vu, Duc-Viet |
| contents | We establish a relation between Lelong numbers and the full mass property of relative non-pluripolar products. We use it to show that if the restricted volume of a big cohomology class $α$ in a compact Kähler $n$-dimensional manifold $X$ to an effective divisor $D$ is of full mass, then the Lelong numbers of the non-pluripolar class $\langle α^{n-1}\rangle$ at every point in the support of $D$ is zero. In particular, we obtain that on projective manifolds, the Lelong numbers of the non-pluripolar class $\langle α^{n-1}\rangle$ of a big class $α$ are zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularity of non-pluripolar cohomology classes Nguyen, Duc-Bao Su, Shuang Vu, Duc-Viet Complex Variables Algebraic Geometry We establish a relation between Lelong numbers and the full mass property of relative non-pluripolar products. We use it to show that if the restricted volume of a big cohomology class $α$ in a compact Kähler $n$-dimensional manifold $X$ to an effective divisor $D$ is of full mass, then the Lelong numbers of the non-pluripolar class $\langle α^{n-1}\rangle$ at every point in the support of $D$ is zero. In particular, we obtain that on projective manifolds, the Lelong numbers of the non-pluripolar class $\langle α^{n-1}\rangle$ of a big class $α$ are zero. |
| title | Singularity of non-pluripolar cohomology classes |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2508.14669 |