caa a22 4500 445836407 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0631-7 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0631-7 van Coevering Craig Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA, USA aut Examples of asymptotically conical Ricci-flat Kähler manifolds [Elektronische Daten] [Craig van Coevering] Previously the author has proved that a crepant resolution π : Y → X of a Ricci-flat Kähler cone X admits a complete Ricci-flat Kähler metric asymptotic to the cone metric in every Kähler class in $${H^2_c(Y,\mathbb R)}$$. These manifolds can be considered to be 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. We concentrate on 3-dimensional examples. Two families of hypersurface examples are given which are distinguished by the condition b 3(Y) = 0 or b 3(Y) ≠ 0. Springer-Verlag, 2009 Calabi-Yau manifold nationallicence Sasaki manifold nationallicence Einstein metric nationallicence Ricci-flat manifold nationallicence Toric varieties nationallicence Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 465-496 0025-5874 267:1-2<465 2011 267 209 https://doi.org/10.1007/s00209-009-0631-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0631-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- van Coevering Craig Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA, USA aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 465-496 0025-5874 267:1-2<465 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer