Momentum construction on Ricci-flat Kähler cones

The Stability Inequality for Ricci-flat Cones

In this article, we thoroughly investigate the stability inequality for Ricci-flat cones. Perhaps most importantly, we prove that the Ricci-flat cone over CP 2 is stable, showing that the first stable non-flat Ricci-flat cone occurs in the smallest possible dimension. On the other hand, we prove that many other examples of Ricci-flat cones over 4-manifolds are unstable, and that Ricci-flat cone...

ADIABATIC LIMITS OF RICCI - FLAT KÄHLER METRICS 3 from

We study adiabatic limits of Ricci-flat Kähler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampère equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metri...

Resolutions of non-regular Ricci-flat Kähler cones

We present explicit constructions of complete Ricci-flat Kähler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kähler-Einstein manifold (V, gV ) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kähler metrics on the total spaces of (i) holomorphic C/Zp orbifold fibrations...

Baryonic branches and resolutions of Ricci-flat Kähler cones

We consider deformations of N = 1 superconformal field theories that are AdS/CFT dual to Type IIB string theory on Sasaki-Einstein manifolds, characterised by non-zero vacuum expectation values for certain baryonic operators. Such baryonic branches are constructed from (partially) resolved, asymptotically conical Ricci-flat Kähler manifolds, together with a choice of point where the stack of D3...

Ricci Flow on Kähler-einstein Surfaces