Forms and Complex Manifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912696264294400 |
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| author | Bisi, Cinzia Cascini, Paolo Tasin, Luca |
| author_facet | Bisi, Cinzia Cascini, Paolo Tasin, Luca |
| contents | We study the intersection form $F_X$ on the second cohomology group $H^2(X, \mathbb{Z})$ of a compact Kähler manifold $X$ of dimension $n$. Although the structure of $F_X$ is relatively well understood in dimensions two and three, much less is known for $n \geq 4$. We investigate the fundamental properties of $F_X$ in higher dimensions and discuss several applications to birational geometry. Finally, we present a number of open problems concerning the relationship between birational invariants and topological invariants of Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forms and Complex Manifolds Bisi, Cinzia Cascini, Paolo Tasin, Luca Algebraic Geometry Complex Variables Differential Geometry 14J50 We study the intersection form $F_X$ on the second cohomology group $H^2(X, \mathbb{Z})$ of a compact Kähler manifold $X$ of dimension $n$. Although the structure of $F_X$ is relatively well understood in dimensions two and three, much less is known for $n \geq 4$. We investigate the fundamental properties of $F_X$ in higher dimensions and discuss several applications to birational geometry. Finally, we present a number of open problems concerning the relationship between birational invariants and topological invariants of Kähler manifolds. |
| title | Forms and Complex Manifolds |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14J50 |
| url | https://arxiv.org/abs/2511.06484 |