Resolutions of non-regular Ricci-flat Kahler cones

Abstract

We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V,g_V) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kahler metrics on the total spaces of (i) holomorphic C^2/Z_p orbifold fibrations over V, (ii) holomorphic orbifold fibrations over weighted projective spaces WCP^1, with generic fibres being the canonical complex cone over V, and (iii) the canonical orbifold line bundle over a family of Fano orbifolds. As special cases, we also obtain smooth complete Ricci-flat Kahler metrics on the total spaces of (a) rank two holomorphic vector bundles over V, and (b) the canonical line bundle over a family of geometrically ruled Fano manifolds with base V. When V=CP^1 our results give Ricci-flat Kahler orbifold metrics on various toric partial resolutions of the cone over the Sasaki-Einstein manifolds Y^{p,q}.

41 pages, 1 figure, v2: cosmetic changes to some equations

References in corpus (9)

• Supersymmetric AdS_5 solutions of M-theory
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Ricci-flat Metrics, Harmonic Forms and Brane Resolutions
• 3-branes on spaces with R x S^2 x S^3 topology
• Kerr-de Sitter Black Holes with NUT Charges
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Explicit Toric Metric on Resolved Calabi-Yau Cone
• A Note on Einstein Sasaki Metrics in D \ge 7
• Resolutions of Cones over Einstein-Sasaki Spaces

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