PreprintCC BY 4.0arXiv
Obstructions to smoothing orbicurves and Orbifold Hecke algebras
Abstract
In this paper, we study obstructions to smoothing nodal orbicurves with orbighosts mapped into cyclic quotient singularities. As an application, we show, under some assumptions, that the orbifold Hecke algebra of a complex global quotient orbifold [X/G] is isomorphic to the degree $0$ cohomology of the A∞-algebra of endomorphisms of a regular cotangent fiber T[x]*[X/G] regarded as an object of the bulk-deformed wrapped Fukaya category of the orbifold T*[X/G] for a compact complex manifold X and finite group G ⊂ Aut(X).
Related
BibTeX
@misc{honda2026obstructions,
title = {{Obstructions to smoothing orbicurves and Orbifold Hecke algebras}},
author = {Ko Honda and Roman Krutowski and Yin Tian and Tianyu Yuan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.11572},
eprint = {2607.11572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11572},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Obstructions to smoothing orbicurves and Orbifold Hecke algebras
AU - Ko Honda
AU - Roman Krutowski
AU - Yin Tian
AU - Tianyu Yuan
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2607.11572
UR - https://arxiv.org/abs/2607.11572
AB - In this paper, we study obstructions to smoothing nodal orbicurves with orbighosts mapped into cyclic quotient singularities. As an application, we show, under some assumptions, that the orbifold Hecke algebra of a complex global quotient orbifold [X/G] is isomorphic to the degree $0$ cohomology of the A_∞-algebra of endomorphisms of a regular cotangent fiber T_[x]^*[X/G] regarded as an object of the bulk-deformed wrapped Fukaya category of the orbifold T^*[X/G] for a compact complex manifold X and finite group G ⊂ Aut(X).
ER -