 

Craig van Coevering
SasakiEinstein 5manifolds associated to toric 3Sasaki manifolds view print


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


Abstract
We give a correspondence between toric 3Sasaki 7manifolds S and certain toric SasakiEinstein 5manifolds M.
These 5manifolds are all diffeomorphic to # k(S^{2}× S^{3}), where k=2b_{2}(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
3Sasaki moment map. It follows that there are infinitely many examples of these toric SasakiEinstein manifolds M for each odd
b_{2}(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 KählerEinstein metrics.
As an application of the proof we determine the local space of antiselfdual structures on a toric antiselfdual Einstein orbifold.


Author information
MaxPlanckInstitut fr Mathematik, Vivatsgasse 7, 53111 Bonn Germany
craigvan@mpimbonn.mpg.de

