Universal curvature bounds on Kähler cones of Calabi–Yau manifolds

Establish universal bounds for the sectional curvatures of the natural Hessian Riemannian metric on the Kähler cone of compact Calabi–Yau manifolds.

Background

The Kähler cone of a compact Calabi–Yau manifold carries a natural Hessian metric given by the potential −log Vol, linking topology and geometry via intersection forms. Wilson proposed a conjecture concerning universal bounds for the sectional curvatures of this metric.

The authors note ongoing work on curvature properties of G2-moduli spaces, motivated by this conjecture in the Calabi–Yau setting, highlighting its relevance to understanding curvature bounds in related moduli problems.

References

There is also ongoing work by Karigiannis and Loftin about the curvatures of the moduli spaces, motivated by the conjectured existence of universal bounds for the sectional curvatures of the Kähler cone of Calabi--Yau manifolds .

— Geometry and periods of $G_2$-moduli spaces  (2410.09987 - Langlais, 2024) in Introduction and motivation (Section 1)