Existence of Hermitian–Yang–Mills metrics under conifold transitions

We first study the degeneration of a sequence ofHermitian–Yang–Mills metrics with respect to a sequenceof balanced metrics on a Calabi–Yau three-fold $\hat{X}$that degenerates to the balanced metric constructed byFu–Li–Yau \cite{FLY} on the complement of finitely many($-1$,$-1$)-curves in $\hat{X}$. Then under someassumptions we show the existence of Hermitian–Yang–Millsmetrics on bundles with respect to balanced metricsconstructed by Fu–Li–Yau over a family of three-folds$X_t$ with trivial canonical bundles. These three-folds$X_t$ are obtained by performing conifold transitionson~$\hat{X}$.

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Published 11 September 2012