Divisors and curves on logarithmic mapping spaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929313985593344 |
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| author | Kennedy-Hunt, Patrick Nabijou, Navid Shafi, Qaasim Zheng, Wanlong |
| author_facet | Kennedy-Hunt, Patrick Nabijou, Navid Shafi, Qaasim Zheng, Wanlong |
| contents | We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00630 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Divisors and curves on logarithmic mapping spaces Kennedy-Hunt, Patrick Nabijou, Navid Shafi, Qaasim Zheng, Wanlong Algebraic Geometry 14H10, 14N35, 14A21, 14C25, 14C20, 14C22 We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study. |
| title | Divisors and curves on logarithmic mapping spaces |
| topic | Algebraic Geometry 14H10, 14N35, 14A21, 14C25, 14C20, 14C22 |
| url | https://arxiv.org/abs/2209.00630 |