New York Journal of Mathematics
Volume 18 (2012) 555-608


Craig van Coevering

Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds

view    print

Published: August 7, 2012
Keywords: Sasaki-Einstein, toric variety, 3-Sasaki manifold
Subject: Primary 53C25, Secondary 53C55, 14M25

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(S2× S3), where k=2b2(S)+1, and are given by a pencil of Sasaki embeddings, where M⊂S is given concretely by the zero set of a component of the 3-Sasaki moment map. It follows that there are infinitely many examples of these toric Sasaki-Einstein manifolds M for each odd b2(M)>1. This is proved by determining the invariant divisors of the twistor space Z of S, and showing that the irreducible such divisors admit orbifold Kähler-Einstein metrics.

As an application of the proof we determine the local space of anti-self-dual structures on a toric anti-self-dual Einstein orbifold.

Author information

Max-Planck-Institut fr Mathematik, Vivatsgasse 7, 53111 Bonn Germany