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PreprintCC BY 4.0arXiv

Compactification of SL(3,ℂ)-Character Varieties of Surfaces via Skein Algebras

  • Seong Youn Kim
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Abstract

We investigate the filtration structure of the skein algebra induced by the (quantum) trace map. Utilizing the structure, we prove that relative SL(3, ℂ) character varieties of punctured surfaces admit log Calabi-Yau compactifications and prove the (weak) geometric P=W conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026compactification,
  title = {{Compactification of $\operatornameSL(3,\mathbbC)$-Character Varieties of Surfaces via Skein Algebras}},
  author = {Seong Youn Kim},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30217},
  eprint = {2608.30217},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30217},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Compactification of SL(3,ℂ)-Character Varieties of Surfaces via Skein Algebras
AU  - Seong Youn Kim
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30217
UR  - https://arxiv.org/abs/2608.30217
AB  - We investigate the filtration structure of the skein algebra induced by the (quantum) trace map. Utilizing the structure, we prove that relative SL(3, ℂ) character varieties of punctured surfaces admit log Calabi-Yau compactifications and prove the (weak) geometric P=W conjecture.
ER  -