A series of Nash resolutions of a singular foliation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917434854735872 |
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| author | Louis, Ruben |
| author_facet | Louis, Ruben |
| contents | We construct a series of blowups $(\widetilde M_i,π_i)_{i\in \mathbb N_0}$ of a singular foliation by applying to the universal Lie $\infty$-algebroid of a singular foliation the so-called Nash modification. For $i=0$, we recover a blowup introduced Sinan Sertöz, and for $i=1$, we recover a notion due to Omar Mohsen. One of the important features is that any singular foliation becomes a Debord foliation (= projective singular foliation) after one blowup. Examples are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08706 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A series of Nash resolutions of a singular foliation Louis, Ruben Differential Geometry 53-XX, 53D17, 32S45, 17B66, 18G10, 53C12, 18G35 We construct a series of blowups $(\widetilde M_i,π_i)_{i\in \mathbb N_0}$ of a singular foliation by applying to the universal Lie $\infty$-algebroid of a singular foliation the so-called Nash modification. For $i=0$, we recover a blowup introduced Sinan Sertöz, and for $i=1$, we recover a notion due to Omar Mohsen. One of the important features is that any singular foliation becomes a Debord foliation (= projective singular foliation) after one blowup. Examples are also given. |
| title | A series of Nash resolutions of a singular foliation |
| topic | Differential Geometry 53-XX, 53D17, 32S45, 17B66, 18G10, 53C12, 18G35 |
| url | https://arxiv.org/abs/2301.08706 |