Stability of the tangent bundle through conifold transitions. (English) Zbl 1536.81005
Summary: Let \(X\) be a compact, Kähler, Calabi-Yau threefold and suppose \(X\mapsto \underline{X}\leadsto X_t\), for \(t\in \Delta\), 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 \(|t|\ll 1\) sufficiently small, the tangent bundle \(T^{1,0}X_t\) 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 \(t\rightarrow 0\).
© 2023 Wiley Periodicals LLC.
© 2023 Wiley Periodicals LLC.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 60J35 | Transition functions, generators and resolvents |
| 14H15 | Families, moduli of curves (analytic) |
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
| 58A30 | Vector distributions (subbundles of the tangent bundles) |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 53C18 | Conformal structures on manifolds |
| 53C38 | Calibrations and calibrated geometries |
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