A polyptych of multi-centered deformation spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915032201166848 |
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| author | Dubouloz, Adrien Mayeux, Arnaud |
| author_facet | Dubouloz, Adrien Mayeux, Arnaud |
| contents | We study deformation spaces using multi-centered dilatations. Interpolating Fulton simple deformation space and Rost asymmetric double deformation space, we introduce (asymmetric) deformation spaces attached to chains of immersions of arbitrary lengths. One of the main results of this paper is the so-called panelization isomorphism, producing several isomorphisms between the deformation space of length $n$ and deformation spaces of smaller lengths. Combining these isomorphisms, we get a polyptych $\mathscr{P}(n)$ of deformation spaces. Having these panelization isomorphisms allows to compute the strata -- certain restrictions of special interests -- of deformation spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A polyptych of multi-centered deformation spaces Dubouloz, Adrien Mayeux, Arnaud Algebraic Geometry We study deformation spaces using multi-centered dilatations. Interpolating Fulton simple deformation space and Rost asymmetric double deformation space, we introduce (asymmetric) deformation spaces attached to chains of immersions of arbitrary lengths. One of the main results of this paper is the so-called panelization isomorphism, producing several isomorphisms between the deformation space of length $n$ and deformation spaces of smaller lengths. Combining these isomorphisms, we get a polyptych $\mathscr{P}(n)$ of deformation spaces. Having these panelization isomorphisms allows to compute the strata -- certain restrictions of special interests -- of deformation spaces. |
| title | A polyptych of multi-centered deformation spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.15606 |