Calabi-Yau structures and Einstein-Sasakian structures on crepant resolutions of isolated singularities

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Abstract

Let <i>X</i><sub>0</sub> be an affine variety with only normal isolated singularity at <i>p</i>. We assume that the complement <i>X</i><sub>0</sub> \ {<i>p</i>} is biholomorphic to the cone <i>C</i>(<i>S</i>) of an Einstein-Sasakian manifold <i>S</i> of real dimension 2<i>n</i> − 1. If there is a resolution of singularity π: <i>X</i> → <i>X</i><sub>0</sub> with trivial canonical line bundle <i>K</i><sub><i>X</i></sub>, then there is a Ricci-flat complete Kähler metric for every Kähler class of <i>X</i>. We also obtain a uniqueness theorem of Ricci-flat conical Kähler metrics in each Kähler class with a certain boundary condition. We show there are many examples of Ricci-flat complete Kähler manifolds arising as crepant resolutions.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 64(3), 1005-1052, 2012-07-01

    The Mathematical Society of Japan

References:  41

Codes

  • NII Article ID (NAID)
    10031177259
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    023829539
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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