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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/2408.00519 |
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| _version_ | 1866914895963881472 |
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| author | Wu, Dongjian Zhang, Nantao |
| author_facet | Wu, Dongjian Zhang, Nantao |
| contents | We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the global dimension, as defined in arXiv:2008.00282 and arXiv:1807.00469, is 3 for any stability condition on $\mathbb P^3$ constructed in arXiv:1410.1585. Finally, we formulate a conjecture concerning the contractibility of a principal connected component of $\mathrm{Stab}(\mathbb P^3)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability Conditions on $\mathbb P^3$ Wu, Dongjian Zhang, Nantao Algebraic Geometry We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the global dimension, as defined in arXiv:2008.00282 and arXiv:1807.00469, is 3 for any stability condition on $\mathbb P^3$ constructed in arXiv:1410.1585. Finally, we formulate a conjecture concerning the contractibility of a principal connected component of $\mathrm{Stab}(\mathbb P^3)$. |
| title | Stability Conditions on $\mathbb P^3$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.00519 |