Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones

Chen, Xuemiao; Sun, Song

doi:10.48550/arxiv.1912.09561

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Quantitative Convergence To the Tangent Cone1

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2021

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“…Related results for stationary Yang-Mills connections were obtained by Yang using a Lojasiewicz inequality [84]. Chen-Sun [12,13,14,15] obtained a general characterization tangent cones of Hermitian-Yang-Mills connections on reflexive sheaves on the ball in C n without estimates for the convergence rate. For our applications, the polynomial decay rate, as well as the convergence at the level of metrics (rather than connections) obtained in Theorem 4.1 is crucial.…”

Section: Quantitative Convergence To the Tangent Conementioning

confidence: 93%

Stability of the tangent bundle through conifold transitions

Collins¹,

Picard²,

Yau³

2021

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Let X be a compact, Kähler, Calabi-Yau threefold and suppose X → X Xt , for t ∈ ∆, 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 1,0 Xt admits a Hermitian-Yang-Mills metric Ht with respect to the conformally balanced metrics constructed by Fu-Li-Yau. Furthermore, we describe the behavior of Ht near the vanishing cycles of Xt as t → 0.

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