Codimension of jumping loci
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912348063662080 |
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| author | Lehmann, Brian Riedl, Eric Tanimoto, Sho |
| author_facet | Lehmann, Brian Riedl, Eric Tanimoto, Sho |
| contents | Suppose that $\mathcal{E}$ is a vector bundle on a smooth projective variety $X$. Given a family of curves $C$ on $X$, we study how the Harder-Narasimhan filtration of $\mathcal{E}|_{C}$ changes as we vary $C$ in our family. Heuristically we expect that the locus where the slopes in the Harder-Narasimhan filtration jump by $μ$ should have codimension which depends linearly on $μ$. We identify the geometric properties which determine whether or not this expected behavior holds. We then apply our results to study rank $2$ bundles on $\mathbb{P}^{2}$ and to study singular loci of moduli spaces of curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codimension of jumping loci Lehmann, Brian Riedl, Eric Tanimoto, Sho Algebraic Geometry Suppose that $\mathcal{E}$ is a vector bundle on a smooth projective variety $X$. Given a family of curves $C$ on $X$, we study how the Harder-Narasimhan filtration of $\mathcal{E}|_{C}$ changes as we vary $C$ in our family. Heuristically we expect that the locus where the slopes in the Harder-Narasimhan filtration jump by $μ$ should have codimension which depends linearly on $μ$. We identify the geometric properties which determine whether or not this expected behavior holds. We then apply our results to study rank $2$ bundles on $\mathbb{P}^{2}$ and to study singular loci of moduli spaces of curves. |
| title | Codimension of jumping loci |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.08759 |