Gopakumar-Vafa invariants associated to cA_n singularities

2025/04/04 by Hao Zhang, Zhang, Hao · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2504.03139

openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper describes Gopakumar-Vafa (GV) invariants associated to cA_n singularities. We (1) generalize GV invariants to crepant partial resolutions of cA_n singularities, (2) show that generalized GV invariants also satisfy Toda's formula and are determined by their associated contraction algebra, (3) give filtration structures on the parameter space of contraction algebras associated to cA_n crepant resolutions with respect to generalized GV invariants, and (4) numerically constrain the possible tuples of GV invariants that can arise. We further give all the tuples that arise from GV invariants of cA₂ crepant resolutions.

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