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arXiv · 2102.11170

Stability of the tangent bundle through conifold transitions

Tristan C. Collins·Sebastien Picard·Shing-Tung Yau
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Abstract

Let $X$ be a compact, K\"ahler, 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 $t\rightarrow 0$.

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Tristan C. Collins, Sebastien Picard, Shing-Tung Yau. 2021-02-22. Stability of the tangent bundle through conifold transitions. https://arxiv.org/abs/2102.11170

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