A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced logarithmic structure, it is possible to desingularise the ma...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
10 Sep 2021
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| Edition: | Version v3 |
| In: |
Arxiv
Year: 2021, Pages: 1-59 |
| DOI: | 10.48550/arXiv.2008.13506 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2008.13506 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2008.13506 
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| Author Notes: | Luca Battistella and Francesca Carocci |
| Summary: | We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced logarithmic structure, it is possible to desingularise the main component by means of a logarithmic modification. Both isolated and non-reduced singularities appear naturally. Our construction gives rise to a notion of reduced Gromov-Witten invariants in genus two. |
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| Item Description: | Version 1 vom 31. August 2020, Version 2 vom 30. Oktober 2020, Version 3 vom 10. September 2021 Gesehen am 06.10.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2008.13506 |