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Existence of Hermitian-Yang-Mills metrics under conifold transitions

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arxiv 1012.3107 v1 pith:ZPBAKDBZ submitted 2010-12-14 math.DG

Ming-Tao Chuan This is my paper · ORCID
classification math.DG
keywords metricshermitian-yang-millsbalancedbundlesconifoldexistencesequencetransitions
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abstract

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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  1. Calabi-Yau threefolds across quadratic singularities

    math.DG 2025-01 unverdicted

    This paper is a survey of the geometry of conifold transitions between Calabi-Yau threefolds, focusing on non-Kähler outputs and the structures they carry.

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