Compactification of $\operatorname{SL}(3,\mathbb{C})$-Character Varieties of Surfaces via Skein Algebras

Seong Youn Kim

paper

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

arXiv:2608.30217

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.

52 pages, 14 figures

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

Abstract

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