Complex Sectional Curvature Blow-Up under Circle Cheeger Collapse

An AIM problem asks whether complex sectional curvatures remain uniformly bounded below in a collapsing circle Cheeger deformation. At a fixed point whose normal circle representation contains rotation blocks of speeds a,b > 0, we derive an exact fixed-point formula. A totally isotropic complex two-plane has K_C(g_ε) = K_C(g) − ab/ε². Thus every fixed component of real codimension at least four forces complex sectional curvature to diverge to −∞. For the standard weight-(1,1) action on the unit round S⁴, the value at either fixed pole is 1 − ε⁻². With only one rotation block, the singular curvature operator is instead rank one and positive semidefinite. The AIM workshop report records the corresponding negative curvature-operator phenomenon but does not identify a complex decomposable direction; the observation here is that its two real negative directions combine into a decomposable totally isotropic bivector. The note is unrefereed and makes no priority claim for this elementary calculation. Research status: Unrefereed preprint released for independent mathematical scrutiny. Publication on Zenodo does not constitute peer review. AI-use disclosure: AI-assisted tools supported literature search, computation, proof auditing, and manuscript preparation. The author remains responsible for all claims and the final text.