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Form-Type Calabi-Yau Equations

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arxiv 0908.0577 v4 pith:EEVDZGKW submitted 2009-08-05 math.DG math.AP

Jixiang Fu , Zhizhang Wang , Damin Wu This is my paper · ORCID
classification math.DGmath.AP
keywords equationbalancedclasshermitianmanifolduniquenessahleraspects
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Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. Solving the equation, one will obtain, in each Bott--Chern cohomology class, a balanced metric which is hermitian Ricci--flat. This can be viewed as a differential form level generalization of the classical Calabi--Yau equation. We establish the existence and uniqueness of the equation on complex tori, and prove certain uniqueness and openness on a general K\"ahler manifold.

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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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