The Tannakian Schottky Conjecture in Genus Five
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913769834151936 |
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| author | Podelski, Constantin |
| author_facet | Podelski, Constantin |
| contents | Using the Tannakian formalism, one can attach to a principally polarized abelian variety a reductive group, along with a representation. We show that this group and the representation characterize Jacobians in genus up to $5$. More generally, our results hold on the bielliptic Prym locus in all genera. This gives the first evidence towards a recent conjecture by Weissauer and Krämer. The main tool in our proof is a criterion for detecting Jacobians relying on Chern-Mather classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tannakian Schottky Conjecture in Genus Five Podelski, Constantin Algebraic Geometry 14H42 Using the Tannakian formalism, one can attach to a principally polarized abelian variety a reductive group, along with a representation. We show that this group and the representation characterize Jacobians in genus up to $5$. More generally, our results hold on the bielliptic Prym locus in all genera. This gives the first evidence towards a recent conjecture by Weissauer and Krämer. The main tool in our proof is a criterion for detecting Jacobians relying on Chern-Mather classes. |
| title | The Tannakian Schottky Conjecture in Genus Five |
| topic | Algebraic Geometry 14H42 |
| url | https://arxiv.org/abs/2501.07512 |