Deformation to the normal bundle and blow-ups via derived Weil restrictions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914169445416960 |
|---|---|
| author | Hekking, Jeroen Khan, Adeel A. Rydh, David |
| author_facet | Hekking, Jeroen Khan, Adeel A. Rydh, David |
| contents | We develop an analogue of the deformation to the normal cone in the context of derived algebraic geometry. This provides any given morphism of derived stacks with a degeneration to the zero section of its normal bundle (i.e., its 1-shifted relative tangent bundle). The construction is realized via the derived Weil restriction along the zero section of the affine line. We prove a general algebraicity theorem for derived Weil restrictions along finite but possibly non-flat morphisms. As an application of the theory, we study derived blow-ups along arbitrary closed centres, generalizing previous works of the authors in the quasi-smooth case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformation to the normal bundle and blow-ups via derived Weil restrictions Hekking, Jeroen Khan, Adeel A. Rydh, David Algebraic Geometry 14A30 (Primary) 14A20, 14D23, 14N35 (Secondary) We develop an analogue of the deformation to the normal cone in the context of derived algebraic geometry. This provides any given morphism of derived stacks with a degeneration to the zero section of its normal bundle (i.e., its 1-shifted relative tangent bundle). The construction is realized via the derived Weil restriction along the zero section of the affine line. We prove a general algebraicity theorem for derived Weil restrictions along finite but possibly non-flat morphisms. As an application of the theory, we study derived blow-ups along arbitrary closed centres, generalizing previous works of the authors in the quasi-smooth case. |
| title | Deformation to the normal bundle and blow-ups via derived Weil restrictions |
| topic | Algebraic Geometry 14A30 (Primary) 14A20, 14D23, 14N35 (Secondary) |
| url | https://arxiv.org/abs/2511.19412 |