Hodge loci associated with linear subspaces intersecting in codimension one
| Autor: | Kloosterman, Remke |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $X\subset \mathbb{P}^{2k+1}$ be a smooth hypersurface containing two k-dimensional linear spaces $\Pi_1,\Pi_2$ intersecting in codimension one. In this paper we study the question whether the Hodge loci $NL([\Pi_1]+\lambda[\Pi_2])$ and $NL([\Pi_1],[\Pi_2])$ coincide. This turns out to be the case in a neighborhood of $X$ if $X$ is very general on $NL([\Pi_1],[\Pi_2])$, $k>1$ and $\lambda\neq 0,1$. However, there exists a hypersurface $X$ for which $NL([\Pi_1],[\Pi_2])$ is smooth at $X$, but $NL([\Pi_1]+\lambda [\Pi_2])$ is singular for all $\lambda\neq0,1$. We expect that this is due to an embedded component of $NL([\Pi_1]+\lambda[\Pi_2])$. The case $k=1$ was treated before by Dan, in that case $NL([\Pi_1]+\lambda [\Pi_2])$ is nonreduced. Comment: arXiv admin note: text overlap with arXiv:2312.12363 |
| Databáze: | arXiv |
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