Stable pairs and the HOMFLY polynomial

• 成果类型: Article
• 署名作者: Maulik, Davesh
• 署名单位: Columbia University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0624-6
• 发表日期: 2016
• 页码: 787-831
• 关键词: hilbert schemes; hecke algebras; idempotents; points; curve; skein

摘要

Given a planar curve singularity, we prove a conjecture of Oblomkov-Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. More generally, we prove an extension of this conjecture, due to Diaconescu-Hua-Soibelman, relating stable pair invariants on the conifold to the colored HOMFLY polynomial of the algebraic link. Our proof uses wall-crossing techniques to prove a blowup identity on the algebro-geometric side. We prove a matching identity for the colored HOMFLY polynomials of a link using skein-theoretic techniques.