A note on dual abelian varieties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914951285702656 |
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| author | Borówka, Aleksandra Borówka, Paweł |
| author_facet | Borówka, Aleksandra Borówka, Paweł |
| contents | For any non-principal polarisation $D$, we explicitly construct $D$-polarised abelian variety $A$, such that its dual abelian variety is not (abstractly) isomorphic to $A$. For $\dim(A)>3$ the construction includes examples with submaximal Picard number equal to $(\dim(A)-1)^2+1$. As a corollary, we show that a very general non-principally polarised abelian variety is not isomorphic to its dual. Moreover, we show an example of an abelian variety that is isomorphic to its dual, yet it does not admit a principal polarisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02718 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on dual abelian varieties Borówka, Aleksandra Borówka, Paweł Algebraic Geometry 14K02, 14K12 For any non-principal polarisation $D$, we explicitly construct $D$-polarised abelian variety $A$, such that its dual abelian variety is not (abstractly) isomorphic to $A$. For $\dim(A)>3$ the construction includes examples with submaximal Picard number equal to $(\dim(A)-1)^2+1$. As a corollary, we show that a very general non-principally polarised abelian variety is not isomorphic to its dual. Moreover, we show an example of an abelian variety that is isomorphic to its dual, yet it does not admit a principal polarisation. |
| title | A note on dual abelian varieties |
| topic | Algebraic Geometry 14K02, 14K12 |
| url | https://arxiv.org/abs/2311.02718 |