Gopakumar--Vafa invariants associated to $cA_n$ singularities

Hao Zhang (University of Glasgow)

Wednesday 11th June 15:00-16:00
Maths 311B

Abstract

This paper describes Gopakumar--Vafa (GV) invariants associated to $cA_n$ singularities. We (1) generalise GV invariants to crepant partial resolutions of $cA_n$ singularities, (2) show that generalised 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 generalised 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 $cA_2$ crepant resolutions.

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