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Integral and higher-genus quantum McKay correspondence in type D

  • Andrea Brini
  • Jingxiang Ma
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Abstract

We establish Iritani's integral form of the β„‚Γ—-equivariant Crepant Transformation Conjecture (CTC) for the minimal resolution of the surface singularity β„‚2/𝔹𝔻4n, where 𝔹𝔻4n is the binary dihedral group of order 4n. We then use Givental's quantisation formalism to prove the all-genus full-descendent CTC in that case. As an application, we deduce the Bryan-Cadman-Young degree-zero form of the orbifold Gromov-Witten/Donaldson-Thomas correspondence for the Calabi-Yau 3-orbifold [β„‚2/𝔹𝔻4n] Γ— β„‚.

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Cite

BibTeXRIS
BibTeX
@misc{brini2026integral,
  title = {{Integral and higher-genus quantum McKay correspondence in type D}},
  author = {Andrea Brini and Jingxiang Ma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22359},
  eprint = {2610.22359},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22359},
}
RIS
TY  - UNPB
TI  - Integral and higher-genus quantum McKay correspondence in type D
AU  - Andrea Brini
AU  - Jingxiang Ma
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22359
UR  - https://arxiv.org/abs/2610.22359
AB  - We establish Iritani's integral form of the β„‚^Γ—-equivariant Crepant Transformation Conjecture (CTC) for the minimal resolution of the surface singularity β„‚^2/𝔹𝔻_4n, where 𝔹𝔻_4n is the binary dihedral group of order 4n. We then use Givental's quantisation formalism to prove the all-genus full-descendent CTC in that case. As an application, we deduce the Bryan-Cadman-Young degree-zero form of the orbifold Gromov-Witten/Donaldson-Thomas correspondence for the Calabi-Yau 3-orbifold [β„‚^2/𝔹𝔻_4n] Γ— β„‚.
ER  -