Rational Curves on Coindex 3 Fano Varieties
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913488377479168 |
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| author | Jovinelly, Eric Okamura, Fumiya |
| author_facet | Jovinelly, Eric Okamura, Fumiya |
| contents | We describe the moduli space of rational curves on smooth Fano varieties of coindex 3. For varieties of dimension 5 or greater, we prove the moduli space has a single irreducible component for each effective numerical class of curves. For varieties of dimension 4, we describe families of rational curves in terms of Fujita's $a$-invariant. Our results verify Lehmann and Tanimoto's Geometric Manin's Conjecture for all smooth coindex 3 Fano varieties over the complex numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational Curves on Coindex 3 Fano Varieties Jovinelly, Eric Okamura, Fumiya Algebraic Geometry 14H10, 14J45 (Primary) We describe the moduli space of rational curves on smooth Fano varieties of coindex 3. For varieties of dimension 5 or greater, we prove the moduli space has a single irreducible component for each effective numerical class of curves. For varieties of dimension 4, we describe families of rational curves in terms of Fujita's $a$-invariant. Our results verify Lehmann and Tanimoto's Geometric Manin's Conjecture for all smooth coindex 3 Fano varieties over the complex numbers. |
| title | Rational Curves on Coindex 3 Fano Varieties |
| topic | Algebraic Geometry 14H10, 14J45 (Primary) |
| url | https://arxiv.org/abs/2409.00834 |