Truncated factorized perverse sheaves on Sym(C)
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912252399976448 |
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| author | Carnovale, Giovanna Esposito, Francesco Degrassi, Lleonard Rubio y |
| author_facet | Carnovale, Giovanna Esposito, Francesco Degrassi, Lleonard Rubio y |
| contents | Kapranov and Schechtman defined the category FP of factorized perverse sheaves on Sym(C) smooth along the stratification given by multiplicities and with values in a braided monoidal category V. We define for each d\in N the category FP^{\leq d} of factorized perverse sheaves on the disjoint union of Sym^n(C) for n\leq d and the category FP_{\leq d} of factorized perverse sheaves on the open subset of Sym(C) consisting of multi-sets with multiplicities bounded by d. We show that the families (FP^{\leq d})_{d in N} and (FP_{\leq d})_{d in N} fit into systems of categories whose inverse limit is FP, and that for each d the natural restriction functor from FP_{\leq d} to FP^{\leq d} is faithful and compatible with taking the limit. For d=1 we prove that the natural restriction functor is an equivalence and that FP^{\leq 1} and FP_{\leq 1} are equivalent to V. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Truncated factorized perverse sheaves on Sym(C) Carnovale, Giovanna Esposito, Francesco Degrassi, Lleonard Rubio y Algebraic Geometry Category Theory Kapranov and Schechtman defined the category FP of factorized perverse sheaves on Sym(C) smooth along the stratification given by multiplicities and with values in a braided monoidal category V. We define for each d\in N the category FP^{\leq d} of factorized perverse sheaves on the disjoint union of Sym^n(C) for n\leq d and the category FP_{\leq d} of factorized perverse sheaves on the open subset of Sym(C) consisting of multi-sets with multiplicities bounded by d. We show that the families (FP^{\leq d})_{d in N} and (FP_{\leq d})_{d in N} fit into systems of categories whose inverse limit is FP, and that for each d the natural restriction functor from FP_{\leq d} to FP^{\leq d} is faithful and compatible with taking the limit. For d=1 we prove that the natural restriction functor is an equivalence and that FP^{\leq 1} and FP_{\leq 1} are equivalent to V. |
| title | Truncated factorized perverse sheaves on Sym(C) |
| topic | Algebraic Geometry Category Theory |
| url | https://arxiv.org/abs/2502.21213 |