The Ciliberto-Di Gennaro conjecture for $d=5$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909020433940480 |
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| author | Kloosterman, Remke |
| author_facet | Kloosterman, Remke |
| contents | The Ciliberto-Di Gennaro conjecture predicts that a nodal hypersurface of degree $d\geq 3$ with at most $2(d-2)(d-1)$ nodes is either factorial, or contains a plane and has at least $(d-1)^2$ nodes, or contains a quadric surface and has $2(d-2)(d-1)$ nodes. This conjecture is classically known for $d=3,4$. In 2022 the author proved this conjecture for $d\geq 7$ by the author. Kvitko announced a proof for $d=6$ in 2025. In this paper we prove the conjecture for the remaining open value of $d$, namely $d=5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Ciliberto-Di Gennaro conjecture for $d=5$ Kloosterman, Remke Algebraic Geometry The Ciliberto-Di Gennaro conjecture predicts that a nodal hypersurface of degree $d\geq 3$ with at most $2(d-2)(d-1)$ nodes is either factorial, or contains a plane and has at least $(d-1)^2$ nodes, or contains a quadric surface and has $2(d-2)(d-1)$ nodes. This conjecture is classically known for $d=3,4$. In 2022 the author proved this conjecture for $d\geq 7$ by the author. Kvitko announced a proof for $d=6$ in 2025. In this paper we prove the conjecture for the remaining open value of $d$, namely $d=5$. |
| title | The Ciliberto-Di Gennaro conjecture for $d=5$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.05796 |