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On a conjecture of Candelas and de la Ossa

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arxiv 1201.4358 v1 pith:DATG6GUN submitted 2012-01-20 math.DG hep-thmath.AG

Jian Song This is my paper · ORCID
classification math.DGhep-thmath.AG
keywords metriccandelasconjectureossaprojectiveprovevarietyapplication
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abstract

We prove that the metric completion of a canonical Ricci-flat Kahler metric on the nonsingular part of a projective Calabi-Yau variety $X$ with ordinary double point singularities, is a compact metric length space homeomorphic to the projective variety $X$ itself. As an application, we prove a conjecture of Candelas and de la Ossa for conifold flops and transitions.

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  1. Calabi-Yau threefolds across quadratic singularities

    math.DG 2025-01 unverdicted

    This paper is a survey of the geometry of conifold transitions between Calabi-Yau threefolds, focusing on non-Kähler outputs and the structures they carry.

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