Vanishing theorems for Hodge numbers and the Calabi curvature operator
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908351309283328 |
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| author | Broder, Kyle Nienhaus, Jan Petersen, Peter Stanfield, James Wink, Matthias |
| author_facet | Broder, Kyle Nienhaus, Jan Petersen, Peter Stanfield, James Wink, Matthias |
| contents | It is shown that a compact $n$-dimensional Kähler manifold with $\frac{n}{2}$-positive Calabi curvature operator has the rational cohomology of complex projective space. For even $n,$ this is sharp in the sense that the complex quadric with its symmetric metric has $\frac{n}{2}$-nonnegative Calabi curvature operator, yet $b_n =2.$ Furthermore, the compact Kähler manifolds with an $\frac{n}{2}$-nonnegative Calabi curvature operator are classified. In addition, the previously known results for the Kähler curvature operator are improved when the metric is Kähler--Einstein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06870 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vanishing theorems for Hodge numbers and the Calabi curvature operator Broder, Kyle Nienhaus, Jan Petersen, Peter Stanfield, James Wink, Matthias Differential Geometry Complex Variables 32Q10, 32Q15, 32Q20, 53C21, 53C55 It is shown that a compact $n$-dimensional Kähler manifold with $\frac{n}{2}$-positive Calabi curvature operator has the rational cohomology of complex projective space. For even $n,$ this is sharp in the sense that the complex quadric with its symmetric metric has $\frac{n}{2}$-nonnegative Calabi curvature operator, yet $b_n =2.$ Furthermore, the compact Kähler manifolds with an $\frac{n}{2}$-nonnegative Calabi curvature operator are classified. In addition, the previously known results for the Kähler curvature operator are improved when the metric is Kähler--Einstein. |
| title | Vanishing theorems for Hodge numbers and the Calabi curvature operator |
| topic | Differential Geometry Complex Variables 32Q10, 32Q15, 32Q20, 53C21, 53C55 |
| url | https://arxiv.org/abs/2503.06870 |