Relate the paper’s Chen–Ruan cohomology approach to Cheltsov–Tschinkel–Zhang (2024) Proposition 2.6

Determine whether the Chen–Ruan cohomology–based obstruction to G-birationality developed in this paper is related to Proposition 2.6 of Cheltsov, Tschinkel, and Zhang (2024, “Equivariant geometry of singular cubic threefolds,” arXiv:2401.10974), and characterize the precise mechanism connecting these results.

Background

The authors recover Example 2.7 of Cheltsov–Tschinkel–Zhang (2024) using their obstruction via Chen–Ruan cohomology and note that deciding linearizability of group actions on nodal cubics is a central difficulty.

They explicitly leave open whether their invariants and methods connect to Proposition 2.6 in the same reference, inviting a comparison or synthesis.

References

We leave open the question of whether the theory developed here can be related to Proposition 2.6 in the same reference.

— A Gromov-Witten approach to $G$-equivariant birational invariants  (2405.07322 - Cavenaghi et al., 2024) in Introduction