Orbifold Euler Characteristics of Compactified Jacobians
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913840069869568 |
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| author | Wood, Sofia |
| author_facet | Wood, Sofia |
| contents | We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold Euler characteristic agrees with the Euler characteristic of the moduli space of stable, genus 0 curves with 2g+n markings up to a combinatorial factor, and in particular, is independent of the degree d and the choice of degree d universal fine compactified Jacobian. As a special case, we see that the universal fine compactified Jacobians defined by Kass and Pagani, depending on a universal polarization, have orbifold Euler characteristic independent of this choice of polarization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbifold Euler Characteristics of Compactified Jacobians Wood, Sofia Algebraic Geometry 14H10, 14K10 We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold Euler characteristic agrees with the Euler characteristic of the moduli space of stable, genus 0 curves with 2g+n markings up to a combinatorial factor, and in particular, is independent of the degree d and the choice of degree d universal fine compactified Jacobian. As a special case, we see that the universal fine compactified Jacobians defined by Kass and Pagani, depending on a universal polarization, have orbifold Euler characteristic independent of this choice of polarization. |
| title | Orbifold Euler Characteristics of Compactified Jacobians |
| topic | Algebraic Geometry 14H10, 14K10 |
| url | https://arxiv.org/abs/2402.19368 |