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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.00315 |
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| _version_ | 1866910527967461376 |
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| author | Chiodo, Alessandro Holmes, David |
| author_facet | Chiodo, Alessandro Holmes, David |
| contents | We construct a derived pushforward of the r-th root of the universal line bundle over the Picard stack of genus g prestable curves carrying a line bundle. We prove a number of basic properties, and give a formula in terms of standard tautological generators. After pullback, our formula recovers formulae of Mumford, of the first-named author, and of Pagani--Ricolfi--van Zelm. We apply these constructions to prove a conjecture expressing the coefficients of higher powers of r in the so-called `Chiodo classes' to the double ramification cycle, and to give a formula for the r-spin logarithmic double ramification cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00315 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mumford's formula on the universal Picard stack Chiodo, Alessandro Holmes, David Algebraic Geometry We construct a derived pushforward of the r-th root of the universal line bundle over the Picard stack of genus g prestable curves carrying a line bundle. We prove a number of basic properties, and give a formula in terms of standard tautological generators. After pullback, our formula recovers formulae of Mumford, of the first-named author, and of Pagani--Ricolfi--van Zelm. We apply these constructions to prove a conjecture expressing the coefficients of higher powers of r in the so-called `Chiodo classes' to the double ramification cycle, and to give a formula for the r-spin logarithmic double ramification cycle. |
| title | Mumford's formula on the universal Picard stack |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2309.00315 |