Let be a complex projective variety with only canonical singularities and with trivial canonical bundle. Let be an ample line bundle on . Assume that the pair is the flat limit of a family of smooth polarized Calabi-Yau manifolds. Assume that for each singular point there exist a Kähler-Einstein Fano manifold and a positive integer dividing such that is very ample and such that the germ is locally analytically isomorphic to a neighborhood of the vertex of the blow-down of the zero section of . We prove that up to biholomorphism, the unique weak Ricci-flat Kähler metric representing on is asymptotic at a polynomial rate near to the natural Ricci-flat Kähler cone metric on constructed using the Calabi ansatz. In particular, our result applies if is a nodal quintic threefold in . This provides the first known examples of compact Ricci-flat manifolds with non-orbifold isolated conical singularities.
@article{PMIHES_2017__126__73_0, author = {Hein, Hans-Joachim and Sun, Song}, title = {Calabi-Yau manifolds with isolated conical singularities}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {73--130}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {126}, year = {2017}, doi = {10.1007/s10240-017-0092-1}, mrnumber = {3735865}, zbl = {1397.32009}, language = {en}, url = {http://archive.numdam.org/articles/10.1007/s10240-017-0092-1/} }
TY - JOUR AU - Hein, Hans-Joachim AU - Sun, Song TI - Calabi-Yau manifolds with isolated conical singularities JO - Publications Mathématiques de l'IHÉS PY - 2017 SP - 73 EP - 130 VL - 126 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://archive.numdam.org/articles/10.1007/s10240-017-0092-1/ DO - 10.1007/s10240-017-0092-1 LA - en ID - PMIHES_2017__126__73_0 ER -
%0 Journal Article %A Hein, Hans-Joachim %A Sun, Song %T Calabi-Yau manifolds with isolated conical singularities %J Publications Mathématiques de l'IHÉS %D 2017 %P 73-130 %V 126 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://archive.numdam.org/articles/10.1007/s10240-017-0092-1/ %R 10.1007/s10240-017-0092-1 %G en %F PMIHES_2017__126__73_0
Hein, Hans-Joachim; Sun, Song. Calabi-Yau manifolds with isolated conical singularities. Publications Mathématiques de l'IHÉS, Volume 126 (2017), pp. 73-130. doi : 10.1007/s10240-017-0092-1. http://archive.numdam.org/articles/10.1007/s10240-017-0092-1/
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