Existence of Hermitian-Yang-Mills metrics under conifold transitions

Details Existence of Hermitian-Yang-Mills metrics under conifold transitions Existence of Hermitian-Yang-Mills metrics under conifold transitions

2010-12-14

arxiv.org/abs/1012.3107v1

Mathematics

Differential Geometry

Scientific paper

We first study the degeneration of a sequence of Hermitian-Yang-Mills metrics with respect to a sequence of balanced metrics on a Calabi-Yau threefold $\hat{X}$ that degenerates to the balanced metric constructed by Fu, Li, and Yau on the complement of finitely many (-1,-1)-curves in $\hat{X}$. Then under some assumptions we show the existence of Hermitian-Yang-Mills metrics on bundles over a family of threefolds $X_t$ with trivial canonical bundles obtained by performing conifold transitions on $\hat{X}$.

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