Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913208497864704 |
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| author | Viergever, Anna M. |
| author_facet | Viergever, Anna M. |
| contents | Levine has constructed motivic analogues of virtual fundamental classes, living in cohomology of Witt sheaves. We use this to define motivic Donaldson-Thomas invariants $\tilde{I}_n$ for $\mathbb{P}^3$ over $\mathbb{R}$. We show that for $n$ odd, $\tilde{I}_n = 0$ and we compute $\tilde{I}_2 = 10, \tilde{I}_4 = 25$ and $\tilde{I}_6 = -50$. We then make a conjecture about the general case, which could be a motivic analogue of a classical theorem of Maulik-Nekrasov-Okounkov-Pandharipande. The results presented here also form a chapter in the authors thesis, which was submitted on May 30'th, 2023. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09882 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space Viergever, Anna M. Algebraic Geometry 14N35, 14F42 Levine has constructed motivic analogues of virtual fundamental classes, living in cohomology of Witt sheaves. We use this to define motivic Donaldson-Thomas invariants $\tilde{I}_n$ for $\mathbb{P}^3$ over $\mathbb{R}$. We show that for $n$ odd, $\tilde{I}_n = 0$ and we compute $\tilde{I}_2 = 10, \tilde{I}_4 = 25$ and $\tilde{I}_6 = -50$. We then make a conjecture about the general case, which could be a motivic analogue of a classical theorem of Maulik-Nekrasov-Okounkov-Pandharipande. The results presented here also form a chapter in the authors thesis, which was submitted on May 30'th, 2023. |
| title | Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space |
| topic | Algebraic Geometry 14N35, 14F42 |
| url | https://arxiv.org/abs/2312.09882 |