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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.09051 |
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| _version_ | 1866909601810612224 |
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| author | Gallardo, Patricio Schaffler, Luca |
| author_facet | Gallardo, Patricio Schaffler, Luca |
| contents | The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight vector. Among these, there is a toric compactification that generalizes the Losev-Manin moduli space of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. As an application of our work, we show that any $\mathbb{Q}$-factorialization of the blow up at the identity of the torus of the generalized Losev-Manin space is not a Mori dream space for a sufficiently high number of hyperplanes. Additionally, for lines in the plane, we provide a precise description of the wall crossing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit wall crossing for the moduli space of hyperplane arrangements Gallardo, Patricio Schaffler, Luca Algebraic Geometry 14J10, 14D06, 52C35 The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight vector. Among these, there is a toric compactification that generalizes the Losev-Manin moduli space of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. As an application of our work, we show that any $\mathbb{Q}$-factorialization of the blow up at the identity of the torus of the generalized Losev-Manin space is not a Mori dream space for a sufficiently high number of hyperplanes. Additionally, for lines in the plane, we provide a precise description of the wall crossing. |
| title | An explicit wall crossing for the moduli space of hyperplane arrangements |
| topic | Algebraic Geometry 14J10, 14D06, 52C35 |
| url | https://arxiv.org/abs/2405.09051 |