Stability of the tangent bundle through conifold transitions

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‐Y...

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Published inCommunications on pure and applied mathematics Vol. 77; no. 1; pp. 284 - 371
Main Authors Collins, Tristan, Picard, Sebastien, Yau, Shing‐Tung
Format Journal Article
LanguageEnglish
Published New York John Wiley and Sons, Limited 01.01.2024
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Summary: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 .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.22135