Nonzero quantum-Chern eigenvalue conjecture for Fano manifolds

Prove that quantum multiplication by the first Chern class $c_1^{TD}$ has a nonzero eigenvalue in the quantum cohomology of every Fano manifold $D$.

Background

The non-nilpotency condition needed for the paper’s quasi-flat construction follows when quantum multiplication by the first Chern class has a nonzero eigenvalue. The authors state that this property is conjectured for all Fano manifolds and explain that, if true, it would substantially extend the scope of their large-scale-geometric result.

References

This property is conjectured to hold for all Fano manifolds, see .

— Biran decomposition and relative symplectic cohomology  (2610.01334 - Jo et al., 1 Oct 2026) in Section 1, subsection “The large scale geometry of $Ham(M,\\omega)$”