Abstract |
We study a class of asymptotically cylindrical Ricci-flat Kähler metrics
arising on quasiprojective manifolds. Using the Calabi–Yau geometry and
analysis and the Kodaira–Kuranishi–Spencer theory and building up on results
of N.Koiso, we show that under rather general hypotheses any local
asymptotically cylindrical Ricci-flat deformations of such metrics are again
Kähler, possibly with respect to a perturbed complex structure. We also find
the dimension of the moduli space for these local deformations. In the
class of asymptotically cylindrical Ricci-flat metrics on 2n-manifolds, the
holonomy reduction to SU(n) is an open condition.
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