Root stacks and periodic decompositions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913374553505792 |
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| author | Bodzenta, Agnieszka Donovan, Will |
| author_facet | Bodzenta, Agnieszka Donovan, Will |
| contents | For an effective Cartier divisor D on a scheme X we may form an nth root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and X. We show that this decomposition is 2n-periodic. For n=2 this gives a purely triangulated proof of the existence of a known spherical functor, namely the pushforward along the embedding of D. For n>2 we find a higher spherical functor in the sense of recent work of Dyckerhoff, Kapranov and Schechtman. We use a realization of the root stack construction as a variation of GIT, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09888 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Root stacks and periodic decompositions Bodzenta, Agnieszka Donovan, Will Algebraic Geometry Primary 14F08, Secondary 14A20, 14C20, 18G80 For an effective Cartier divisor D on a scheme X we may form an nth root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and X. We show that this decomposition is 2n-periodic. For n=2 this gives a purely triangulated proof of the existence of a known spherical functor, namely the pushforward along the embedding of D. For n>2 we find a higher spherical functor in the sense of recent work of Dyckerhoff, Kapranov and Schechtman. We use a realization of the root stack construction as a variation of GIT, which may be of independent interest. |
| title | Root stacks and periodic decompositions |
| topic | Algebraic Geometry Primary 14F08, Secondary 14A20, 14C20, 18G80 |
| url | https://arxiv.org/abs/2307.09888 |