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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.05571 |
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| _version_ | 1866908754783502336 |
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| author | Wang, Zhenjian |
| author_facet | Wang, Zhenjian |
| contents | Cubic forms $C$ are constructed in the work of R. Aguilar, M. Green and P. Griffiths to establish the generic global Torelli theorem for Fano-K3 pairs $(X,Y)$, where $X: F=0$ is a cubic threefold in $\mathbb{P}^4$ and $Y\in|-K_X|$ is an anticanonical smooth section of $X$ defined by a quadratic form $Q$. In this article, we prove the following two results, which were previously verified with the computer aid of Macaulay2: for a generic pair $(X,Y)$, (i) the cubic form $C$ is smooth; (2) $(J_{F,3}:Q)=0$, and thereby give a precise meaning of the word ``generic" in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05571 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New proofs for technical results in "Infinitesimal invariants of mixed Hodge structures'' (arXiv:2406.17118v1) Wang, Zhenjian Algebraic Geometry Primary 13F20, Secondary 13D40, 13E10 Cubic forms $C$ are constructed in the work of R. Aguilar, M. Green and P. Griffiths to establish the generic global Torelli theorem for Fano-K3 pairs $(X,Y)$, where $X: F=0$ is a cubic threefold in $\mathbb{P}^4$ and $Y\in|-K_X|$ is an anticanonical smooth section of $X$ defined by a quadratic form $Q$. In this article, we prove the following two results, which were previously verified with the computer aid of Macaulay2: for a generic pair $(X,Y)$, (i) the cubic form $C$ is smooth; (2) $(J_{F,3}:Q)=0$, and thereby give a precise meaning of the word ``generic" in this context. |
| title | New proofs for technical results in "Infinitesimal invariants of mixed Hodge structures'' (arXiv:2406.17118v1) |
| topic | Algebraic Geometry Primary 13F20, Secondary 13D40, 13E10 |
| url | https://arxiv.org/abs/2601.05571 |