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DC Field | Value | Language |
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dc.contributor.author | Colombo, E. | - |
dc.contributor.author | Naranjo del Val, Juan Carlos | - |
dc.contributor.author | Pirola, Gian Pietro | - |
dc.date.accessioned | 2022-11-04T11:18:16Z | - |
dc.date.available | 2022-11-04T11:18:16Z | - |
dc.date.issued | 2021-01-12 | - |
dc.identifier.issn | 0025-5831 | - |
dc.identifier.uri | http://hdl.handle.net/2445/190458 | - |
dc.description.abstract | We study the subsets $V_k(A)$ of a complex abelian variety $A$ consisting in the collection of points $x \in A$ such that the zero-cycle $\{x\}-\left\{0_A\right\}$ is $k$-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that $\operatorname{dim} V_k(A) \leq k-1$ and $\operatorname{dim} V_k(A)$ is countable for a very general abelian variety of dimension at least $2 k-1$. We study in particular the locus $\mathcal{V}_{g, 2}$ in the moduli space of abelian varieties of dimension $g$ with a fixed polarization, where $V_2(A)$ is positive dimensional. We prove that an irreducible subvariety $\mathcal{Y} \subset \mathcal{V}_{g, 2}$, $g \geq 3$, such that for a very general $y \in \mathcal{Y}$ there is a curve in $V_2\left(A_y\right)$ generating $A$ satisfies $\operatorname{dim} \mathcal{Y} \leq 2 g-1$. The hyperelliptic locus shows that this bound is sharp. | - |
dc.format.extent | 14 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1007/s00208-020-02134-x | - |
dc.relation.ispartof | Mathematische Annalen, 2021, vol. 381, p. 91-104 | - |
dc.relation.uri | https://doi.org/10.1007/s00208-020-02134-x | - |
dc.rights | cc by (c) Colombo, E. et al., 2021 | - |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Varietats abelianes | - |
dc.subject.classification | Geometria algebraica | - |
dc.subject.classification | Cicles algebraics | - |
dc.subject.other | Abelian varieties | - |
dc.subject.other | Algebraic geometry | - |
dc.subject.other | Algebraic cycles | - |
dc.title | On the dimension of Voisin sets in the moduli space of abelian varieties | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 705384 | - |
dc.date.updated | 2022-11-04T11:18:16Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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