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Group action of Hochschild-Serre algebra and categorical reconstruction
Abstract
We study the action of the Serre functor of smooth proper dg categories at their Hochschild-Serre algebra, and the invariant sub-aglebra of the Serre functor. As applications, we prove some theorems of categorical Torelli. Namely, let Ku(X) be the Kuznetsov component of degree d smooth hypersurface in weighted projective space ℙ(a0, a1, ⋯, an), where the common maximal divisor gcd(d, ∑ni=0ai)=1. We show the categorical Torelli for Ku(X). We show that the ℂ∗ equivariant matrix factorization category associated with a quasi-homogeneous polynomial function f that has an isolated singularity together with a twisted functor {1} reconstructs f up to an isomorphism.
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BibTeX
@misc{lin2026group,
title = {{Group action of Hochschild-Serre algebra and categorical reconstruction}},
author = {Xun Lin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07562},
eprint = {2609.07562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07562},
}
RIS
TY - UNPB
TI - Group action of Hochschild-Serre algebra and categorical reconstruction
AU - Xun Lin
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07562
UR - https://arxiv.org/abs/2609.07562
AB - We study the action of the Serre functor of smooth proper dg categories at their Hochschild-Serre algebra, and the invariant sub-aglebra of the Serre functor. As applications, we prove some theorems of categorical Torelli. Namely, let Ku(X) be the Kuznetsov component of degree d smooth hypersurface in weighted projective space ℙ(a_0, a_1, ⋯, a_n), where the common maximal divisor gcd(d, ∑^n_i=0a_i)=1. We show the categorical Torelli for Ku(X). We show that the ℂ^∗ equivariant matrix factorization category associated with a quasi-homogeneous polynomial function f that has an isolated singularity together with a twisted functor {1} reconstructs f up to an isomorphism.
ER -