The non-abelian Brill-Noether divisor on $\overline{\mathcal{M}}_{13}$ and the Kodaira dimension of $\overline{\mathcal{R}}_{13}$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911833286246400 |
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| author | Farkas, Gavril Jensen, Dave Payne, Sam |
| author_facet | Farkas, Gavril Jensen, Dave Payne, Sam |
| contents | The paper is devoted to highlighting several novel aspects of the moduli space of curves of genus 13, the first genus g where phenomena related to K3 surfaces no longer govern the birational geometry of M_g. We compute the class of the non-abelian Brill-Noether divisor on M_13 of curves that have a stable rank 2 vector bundle with many sections. This provides the first example of an effective divisor on M_g with slope less than 6+10/g. Earlier work on the Slope Conjecture suggested that such divisors may not exist. The main geometric application of our result is a proof that the Prym moduli space of genus 13 is of general type. Among other things, we also prove the Bertram-Feinberg-Mukai and the Strong Maximal Rank Conjectures on M_13 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_09553 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The non-abelian Brill-Noether divisor on $\overline{\mathcal{M}}_{13}$ and the Kodaira dimension of $\overline{\mathcal{R}}_{13}$ Farkas, Gavril Jensen, Dave Payne, Sam Algebraic Geometry The paper is devoted to highlighting several novel aspects of the moduli space of curves of genus 13, the first genus g where phenomena related to K3 surfaces no longer govern the birational geometry of M_g. We compute the class of the non-abelian Brill-Noether divisor on M_13 of curves that have a stable rank 2 vector bundle with many sections. This provides the first example of an effective divisor on M_g with slope less than 6+10/g. Earlier work on the Slope Conjecture suggested that such divisors may not exist. The main geometric application of our result is a proof that the Prym moduli space of genus 13 is of general type. Among other things, we also prove the Bertram-Feinberg-Mukai and the Strong Maximal Rank Conjectures on M_13 |
| title | The non-abelian Brill-Noether divisor on $\overline{\mathcal{M}}_{13}$ and the Kodaira dimension of $\overline{\mathcal{R}}_{13}$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2110.09553 |