The bielliptic locus in genus 11
| Autor: | Canning, Samir, Larson, Hannah |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Chow ring of $\mathcal{M}_g$ is known to be generated by tautological classes for $g \leq 9$. Meanwhile, the first example of a non-tautological class on $\mathcal{M}_{g}$ is the fundamental class of the bielliptic locus in $\mathcal{M}_{12}$, due to van Zelm. It remains open if the Chow rings of $\mathcal{M}_{10}$ and $\mathcal{M}_{11}$ are generated by tautological classes. In these cases, a natural first place to look is at the bielliptic locus. In genus $10$, it is already known that classes supported on the bielliptic locus are tautological. Here, we prove that all classes supported on the bielliptic locus are tautological in genus $11$. By Looijenga's vanishing theorem, this implies that they all vanish. Comment: 14 pages, comments welcome! |
| Databáze: | arXiv |
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