Isosystolic Inequalities for Holomorphic Chains in $\mathbb{C}P^{n}$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909712780361728 |
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| author | Junior, Luciano L. |
| author_facet | Junior, Luciano L. |
| contents | We introduce the \emph{holomorphic $k$-systole} of a Hermitian metric on $\mathbb{C}P^n$, defined as the infimum of areas of homologically non-trivial holomorphic $k$-chains. Our main result establishes that, within the set of Gauduchon metrics, the Fubini-Study metric locally minimizes the volume-normalized holomorphic $(n-1)$-systole. As an application, we construct Gauduchon metrics on $\mathbb{C}P^2$ arbitrarily close to the Fubini-Study metric whose homological $2$-systole is realized by non-holomorphic chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isosystolic Inequalities for Holomorphic Chains in $\mathbb{C}P^{n}$ Junior, Luciano L. Differential Geometry Complex Variables We introduce the \emph{holomorphic $k$-systole} of a Hermitian metric on $\mathbb{C}P^n$, defined as the infimum of areas of homologically non-trivial holomorphic $k$-chains. Our main result establishes that, within the set of Gauduchon metrics, the Fubini-Study metric locally minimizes the volume-normalized holomorphic $(n-1)$-systole. As an application, we construct Gauduchon metrics on $\mathbb{C}P^2$ arbitrarily close to the Fubini-Study metric whose homological $2$-systole is realized by non-holomorphic chains. |
| title | Isosystolic Inequalities for Holomorphic Chains in $\mathbb{C}P^{n}$ |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2507.23156 |