Symplectic Kodaira dimension of the remaining resolutions

Determine the symplectic Kodaira dimension of the minimal symplectic resolutions associated with the remaining cases of Theorem 1.3, including Case (3)(iii).

Background

Theorem 3.5 computes minimality and symplectic Kodaira dimension for several cases arising from the classified pseudofree symplectic actions, and identifies some other resolutions as rational. The remark addresses the cases not covered by those conclusions.

Although the resolutions are known to be non-minimal in all the remaining cases except Case (3)(iii), the paper does not determine their symplectic Kodaira dimensions. Thus the unresolved issue is the classification of these resolutions within symplectic Kodaira-dimension theory.

References

For the remaining cases of Theorem 1.3, the symplectic Kodaira dimension of $X$ is unknown at the moment.

— Symplectic symmetries of a hypothetical exotic $CP^2$: a potential construction or a nonexistence proof  (2610.06746 - Chen, 5 Oct 2026) in Remark 3.6(1), Section 3.2