Stability of the tangent bundle through conifold transitions
Tristan C. Collins, Sébastien Picard, Shing–Tung Yau
Abstract
Abstract Let 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 .
Topics & Concepts
ConifoldMathematicsGravitational singularityPure mathematicsTangent bundleDisjoint setsUnit tangent bundleTangent coneMetric (unit)Mathematical analysisNormal bundleSmoothingHermitian manifoldHermitian matrixTangentCurvatureGeometryMathematical physicsVector bundleTangent spaceGauge theoryOperations managementEconomicsRicci curvatureStatisticsGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAlgebraic Geometry and Number Theory