The tropicalization of the moduli space of curves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2012
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| _version_ | 1866915088151085056 |
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| author | Abramovich, Dan Caporaso, Lucia Payne, Sam |
| author_facet | Abramovich, Dan Caporaso, Lucia Payne, Sam |
| contents | We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the "naive" set-theoretic tropicalization map. The proof passes through general structure results on the skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct tautological forgetful, clutching, and gluing maps between moduli spaces of extended tropical curves and show that they are compatible with the analogous tautological maps in the algebraic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1212_0373 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | The tropicalization of the moduli space of curves Abramovich, Dan Caporaso, Lucia Payne, Sam Algebraic Geometry 14T05, 14H10, 14G22 We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the "naive" set-theoretic tropicalization map. The proof passes through general structure results on the skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct tautological forgetful, clutching, and gluing maps between moduli spaces of extended tropical curves and show that they are compatible with the analogous tautological maps in the algebraic setting. |
| title | The tropicalization of the moduli space of curves |
| topic | Algebraic Geometry 14T05, 14H10, 14G22 |
| url | https://arxiv.org/abs/1212.0373 |