Stability of the tangent bundle through conifold transitions

2021/02/22 by Tristan C. Collins, Sébastien Picard, Collins, Tristan C. +3 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.2102.11170

openalex publication_date 2021/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a compact, Kähler, Calabi-Yau threefold and suppose X↦ \underlineX\leadsto X_t , for t∈ Δ, is a conifold transition obtained by contracting finitely many disjoint (-1,-1) curves in X and then smoothing the resulting ordinary double point singularities. We show that, for |t|≪ 1 sufficiently small, the tangent bundle T^1,0X_t admits a Hermitian-Yang-Mills metric H_t with respect to the conformally balanced metrics constructed by Fu-Li-Yau. Furthermore, we describe the behavior of H_t near the vanishing cycles of X_t as t→ 0.

Cited by

• Singular Gauduchon Conjecture
• Mapping moduli across heterotic conifolds
• An introduction to conifold transitions
• Almost Calabi-Yau with torsion 6-manifolds and the instanton condition

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• An introduction to conifold transitions
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• Hermitian-Yang-Mills connections on some complete non-compact Kähler manifolds
• Invariant Stability Conditions on Certain Calabi-Yau Threefolds