On the Zariski density of rational curves on IHS manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915617088471040 |
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| author | Beri, Pietro Mongardi, Giovanni Pacienza, Gianluca |
| author_facet | Beri, Pietro Mongardi, Giovanni Pacienza, Gianluca |
| contents | In analogy with recent works on $K3$ surfaces, we study the existence of infinitely many ruled divisors on projective irreducible holomorphic symplectic (IHS) manifolds. We prove such an existence result for any projective IHS manifold of $K3^{[n]}$ or generalized Kummer type which is not a variety defined over $\overline{\mathbb{Q}}$ with Picard number one or maximal. The result is obtained as a combination of the regeneration principle and of a generalization to higher dimension of a controlled degeneration technique, invented by Chen, Gounelas and Liedtke in dimension 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Zariski density of rational curves on IHS manifolds Beri, Pietro Mongardi, Giovanni Pacienza, Gianluca Algebraic Geometry 14H45, 14J42 In analogy with recent works on $K3$ surfaces, we study the existence of infinitely many ruled divisors on projective irreducible holomorphic symplectic (IHS) manifolds. We prove such an existence result for any projective IHS manifold of $K3^{[n]}$ or generalized Kummer type which is not a variety defined over $\overline{\mathbb{Q}}$ with Picard number one or maximal. The result is obtained as a combination of the regeneration principle and of a generalization to higher dimension of a controlled degeneration technique, invented by Chen, Gounelas and Liedtke in dimension 2. |
| title | On the Zariski density of rational curves on IHS manifolds |
| topic | Algebraic Geometry 14H45, 14J42 |
| url | https://arxiv.org/abs/2502.09349 |