Truncated factorized perverse sheaves on Sym(C)
Abstract
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.
Keywords
Cite
@article{arxiv.2502.21213,
title = {Truncated factorized perverse sheaves on Sym(C)},
author = {Giovanna Carnovale and Francesco Esposito and Lleonard Rubio y Degrassi},
journal= {arXiv preprint arXiv:2502.21213},
year = {2025}
}