Examples of asymptotically conical Ricci-flat Kähler manifolds
arXiv:0812.4745 · doi:10.1007/s00209-009-0631-7
Abstract
The author has proved that a crepant resolution Y of a Ricci-flat Kähler cone X admits a complete Ricci-flat Kähler metric asymptotic to the cone metric in every Kähler class in H^2_c(Y,\R). These manifolds are generalizations of the Ricci-flat ALE Kähler spaces known by the work of P. Kronheimer, D. Joyce and others. This article considers further the problem of constructing examples. We show that every 3-dimensional Gorenstein toric Kähler cone admits a crepant resolution for which the above theorem applies. This gives infinitely many examples of asymptotically conical Ricci-flat manifolds. Then other examples are given of which are crepant resolutions hypersurface singularities which are known to admit Ricci-flat Kähler cone metrics by the work of C. Boyer, K. Galicki, J. Kollár, and others. Two families of hypersurface examples are given which are distinguished by the condition b_3(Y)=0 or b_3(Y)>0.
32 pages, 1 figure Some material added on embeddings of cones and some minor corrections made
References in corpus (5)
Cited by in corpus (12)
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