Stability of the tangent bundle through conifold transitions

Abstract

AbstractLet X be a compact, Kähler, Calabi‐Yau threefold and suppose , for , is a conifold transition obtained by contracting finitely many disjoint curves in X and then smoothing the resulting ordinary double point singularities. We show that, for sufficiently small, the tangent bundle admits a Hermitian‐Yang‐Mills metric with respect to the conformally balanced metrics constructed by Fu‐Li‐Yau. Furthermore, we describe the behavior of near the vanishing cycles of as .