16 citations · 40 across the 10 of their papers we have counts for
9 papers · 1 filter
Calabi-Yau metrics on canonical bundles of flag varieties
Craig van Coevering
This note gives a simple formula for the unique asymptotically conical Calabi-Yau metrics on the canonical bundle of a flag variety known to exist by the work of R. Goto and others…
Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
Craig van Coevering
We develop some pluripotential theoretic techniques for the transversally holomorphic foliation of a Sasakian manifold. We prove the convexity of the K-energy along weak geodesics…
Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds
Craig van Coevering
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some…
Holomorphic Lagrangian fibrations of toric hyperkahler manifolds
Craig van Coevering, Wei Zhang
For the sake of hyperk{ä}hler SYZ conjecture, finding holomorphic Lagrangian fibrations becomes an important issue. Toric hyperk{ä}hler manifolds are real dimension non-compac…
Cotangent bundles of toric varieties and coverings of toric hyperkähler manifolds
Craig van Coevering, Wei Zhang
Toric hyperk{ä}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, vi…
Regularity of asymptotically conical Ricci-flat Kähler metrics
Craig van Coevering
Using methods of A. Grigor'yan and L. Saloff-Coste we prove that on a manifold with a conical end the heat kernel has a Gaussian bound. This result is applied to asymptotically con…
A Construction of Complete Ricci-flat Kähler Manifolds
Craig van Coevering
We consider an extension of the results of S. Bando, R. Kobyashi, G. Tian, and S. T. Yau on the existence of Ricci-flat Kähler metrics on quasi-projective varieties Y=X\D with α[D]…
Some examples of toric Sasaki-Einstein manifolds
Craig van Coevering
A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uni…
Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds
Craig van Coevering
We give a correspondence between toric 3-Sasaki 7-manifolds S and certain toric Sasaki-Einstein 5-manifolds M. These 5-manifolds are all diffeomorphic to k#(S^2\times S^3), where k…