The monodromy of families of subvarieties on abelian varieties
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909541105401856 |
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| author | Javanpeykar, Ariyan Krämer, Thomas Lehn, Christian Maculan, Marco |
| author_facet | Javanpeykar, Ariyan Krämer, Thomas Lehn, Christian Maculan, Marco |
| contents | Motivated by recent work of Lawrence-Venkatesh and Lawrence-Sawin, we show that non-isotrivial families of subvarieties in abelian varieties have big monodromy when twisted by generic rank one local systems. While Lawrence-Sawin discuss the case of subvarieties of codimension one, our results hold for subvarieties of codimension at least half the dimension of the ambient abelian variety. For the proof, we use a combination of geometric arguments and representation theory to show that the Tannaka groups of intersection complexes on such subvarieties are big. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_05166 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The monodromy of families of subvarieties on abelian varieties Javanpeykar, Ariyan Krämer, Thomas Lehn, Christian Maculan, Marco Algebraic Geometry Number Theory Motivated by recent work of Lawrence-Venkatesh and Lawrence-Sawin, we show that non-isotrivial families of subvarieties in abelian varieties have big monodromy when twisted by generic rank one local systems. While Lawrence-Sawin discuss the case of subvarieties of codimension one, our results hold for subvarieties of codimension at least half the dimension of the ambient abelian variety. For the proof, we use a combination of geometric arguments and representation theory to show that the Tannaka groups of intersection complexes on such subvarieties are big. |
| title | The monodromy of families of subvarieties on abelian varieties |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2210.05166 |