Equivariant Contact Darboux Quotients
Abstract
We prove an equivariant Darboux theorem for −1-shifted contact derived Artin stacks. Such a stack admits a smooth atlas by contact Darboux charts: the derived discriminant locus Δloc(s) of a relative section s, extended in degree −2 along the relative dimension of the chart. Near a point with linearly reductive stabilizer G acting on the contact line through a character χ, the stack is étale-locally the quotient [ΔlocG(s)/G], whose degree −2 generators are indexed by the Lie algebra of G with differential a contact moment map. The cotangent complex sees these generators as Lie ker(χ) in degree −2; they vanish exactly when ker(χ) is finite, and the quotient of the discriminant locus alone is a local model at no point where they are nonzero. For a quiver with potential the contact moment map is the moment map of the doubled quiver, the classical truncation is the representation space of the Jacobi algebra, and the degree −2 generators are carried exactly by the locus of positive-dimensional stabilizer.
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BibTeX
@misc{izbudak2026equivariant,
title = {{Equivariant Contact Darboux Quotients}},
author = {Efe İzbudak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.11179},
eprint = {2606.11179},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.11179},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Equivariant Contact Darboux Quotients
AU - Efe İzbudak
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2606.11179
UR - https://arxiv.org/abs/2606.11179
AB - We prove an equivariant Darboux theorem for −1-shifted contact derived Artin stacks. Such a stack admits a smooth atlas by contact Darboux charts: the derived discriminant locus Δloc(s) of a relative section s, extended in degree −2 along the relative dimension of the chart. Near a point with linearly reductive stabilizer G acting on the contact line through a character χ, the stack is étale-locally the quotient [Δloc_G(s)/G], whose degree −2 generators are indexed by the Lie algebra of G with differential a contact moment map. The cotangent complex sees these generators as Lie ker(χ) in degree −2; they vanish exactly when ker(χ) is finite, and the quotient of the discriminant locus alone is a local model at no point where they are nonzero. For a quiver with potential the contact moment map is the moment map of the doubled quiver, the classical truncation is the representation space of the Jacobi algebra, and the degree −2 generators are carried exactly by the locus of positive-dimensional stabilizer.
ER -