GIT for root stacks and 3d mirror symmetry

@misc{garg2026root,
  title = {{GIT for root stacks and 3d mirror symmetry}},
  author = {Swapnil Garg and Ruoxi Li and Yuji Okitani},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30350},
  eprint = {2608.30350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30350},
}

TY  - UNPB
TI  - GIT for root stacks and 3d mirror symmetry
AU  - Swapnil Garg
AU  - Ruoxi Li
AU  - Yuji Okitani
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30350
UR  - https://arxiv.org/abs/2608.30350
AB  - Using window theory, Bodzenta--Donovan showed that the derived category of a root stack √[n]X/D has a 2n-periodic $2$-term semiorthogonal decomposition. We define a categorical generalization of the root stack construction and interpret this as a pullback on the B-side of the 3d mirror symmetry equivalence of Gammage--Hilburn--Mazel-Gee. We analyze this pullback using categorical representation theoretic results of Ben-Zvi--Francis--Nadler and Ben-Zvi--Nadler--Preygel applied to SODs. We also show that the pullback is equivalent to a pushforward of perverse schobers on the A-side, allowing us to deduce periodicity from a simple decomposition of an A-side Lagrangian skeleton. Additionally, we adapt the construction of Bodzenta--Donovan to a new GIT problem, which yields an embedding of Coh(√[m]X/D) into Coh(√[n]X/D) for m<n coprime, and prove 2n-periodicity of the resulting $2$-term SOD.
ER  -