On a conjecture on Hodge loci of linear combinations of linear subvarieties
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916845733281792 |
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| author | Kloosterman, Remke |
| author_facet | Kloosterman, Remke |
| contents | For each $k \geq 5$ we give a counterexample to a conjecture of Movasati on the dimension of certain Hodge loci of cubic hypersurfaces in $\mathbf{P}^{2k+1}$ containing two $k$-planes intersecting in dimension $k-3$. We give similar examples for Hodge loci of cubic hypersurfaces in $\mathbf{P}^{2k+1}$ containing two $k$-planes intersecting in dimension $k-2$ and for quartic hypersurfaces in $\mathbf{P}^{2k+1}$ containing two $k$-planes intersecting in dimension $k-2$.
Moreover, we present new evidence for Movasati's conjecture for the values of $k$ for which our type of counterexamples cannot exist, i.e., for $k=3,4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a conjecture on Hodge loci of linear combinations of linear subvarieties Kloosterman, Remke Algebraic Geometry For each $k \geq 5$ we give a counterexample to a conjecture of Movasati on the dimension of certain Hodge loci of cubic hypersurfaces in $\mathbf{P}^{2k+1}$ containing two $k$-planes intersecting in dimension $k-3$. We give similar examples for Hodge loci of cubic hypersurfaces in $\mathbf{P}^{2k+1}$ containing two $k$-planes intersecting in dimension $k-2$ and for quartic hypersurfaces in $\mathbf{P}^{2k+1}$ containing two $k$-planes intersecting in dimension $k-2$. Moreover, we present new evidence for Movasati's conjecture for the values of $k$ for which our type of counterexamples cannot exist, i.e., for $k=3,4$. |
| title | On a conjecture on Hodge loci of linear combinations of linear subvarieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.12363 |