Bott-Chern complexity of Kähler pairs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908352833912832 |
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| author | Hacon, Christopher Moraga, Joaquín Yáñez, José Ignacio |
| author_facet | Hacon, Christopher Moraga, Joaquín Yáñez, José Ignacio |
| contents | We introduce the Bott-Chern complexity of a compact Kähler pair $(X,B)$. This invariant compares $\dim(X)$, $\dim H^{1,1}_{\rm BC}(X)$ and the sum of the coefficients of $B$. When $(X,B)$ is Calabi-Yau, we show that its Bott-Chern complexity is non-negative. We prove that the Bott-Chern complexity of a Calabi-Yau compact Kähler pair $(X,B)$ is at least three whenever $X$ is not projective. Furthermore, we show this value is optimal and is achieved by certain singular non-projective K3 surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bott-Chern complexity of Kähler pairs Hacon, Christopher Moraga, Joaquín Yáñez, José Ignacio Algebraic Geometry Complex Variables Primary: 32J27, 14E30, Secondary: 14M25, 14J28 We introduce the Bott-Chern complexity of a compact Kähler pair $(X,B)$. This invariant compares $\dim(X)$, $\dim H^{1,1}_{\rm BC}(X)$ and the sum of the coefficients of $B$. When $(X,B)$ is Calabi-Yau, we show that its Bott-Chern complexity is non-negative. We prove that the Bott-Chern complexity of a Calabi-Yau compact Kähler pair $(X,B)$ is at least three whenever $X$ is not projective. Furthermore, we show this value is optimal and is achieved by certain singular non-projective K3 surfaces. |
| title | Bott-Chern complexity of Kähler pairs |
| topic | Algebraic Geometry Complex Variables Primary: 32J27, 14E30, Secondary: 14M25, 14J28 |
| url | https://arxiv.org/abs/2505.04303 |