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| Main Authors: | , , |
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| Format: | Preprint |
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2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1204.1435 |
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| _version_ | 1866916196547297280 |
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| author | Checcoli, Sara Veneziano, Francesco Viada, Evelina |
| author_facet | Checcoli, Sara Veneziano, Francesco Viada, Evelina |
| contents | A deep conjecture on torsion anomalous varieties states that if $V$ is a weak-transverse variety in an abelian variety, then the complement $V^{ta}$ of all $V$-torsion anomalous varieties is open and dense in $V$. We prove some cases of this conjecture. We show that the $V$-torsion anomalous varieties of relative codimension one are non-dense in any weak-transverse variety $V$ embedded in a product of elliptic curves with CM. We give explicit uniform bounds in the dependence on $V$. As an immediate consequence we prove the conjecture for $V$ of codimension two in a product of CM elliptic curves. We also point out some implications on the effective Mordell-Lang Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1204_1435 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | On torsion anomalous intersections Checcoli, Sara Veneziano, Francesco Viada, Evelina Number Theory 11G50, 14G40 A deep conjecture on torsion anomalous varieties states that if $V$ is a weak-transverse variety in an abelian variety, then the complement $V^{ta}$ of all $V$-torsion anomalous varieties is open and dense in $V$. We prove some cases of this conjecture. We show that the $V$-torsion anomalous varieties of relative codimension one are non-dense in any weak-transverse variety $V$ embedded in a product of elliptic curves with CM. We give explicit uniform bounds in the dependence on $V$. As an immediate consequence we prove the conjecture for $V$ of codimension two in a product of CM elliptic curves. We also point out some implications on the effective Mordell-Lang Conjecture. |
| title | On torsion anomalous intersections |
| topic | Number Theory 11G50, 14G40 |
| url | https://arxiv.org/abs/1204.1435 |