Deformations of Compact Calabi--Yau Conifolds

Yohsuke Imagi

Deformations of Compact Calabi--Yau Conifolds

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arxiv 2504.03243 v2 pith:PPCIN7V2 submitted 2025-04-04 math.AG math.CVmath.DG

Yohsuke Imagi This is my paper

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abstract

Let $X$ be a compact normal K\"ahler space whose canonical sheaf is a rank-one free $\mathcal O_X$ module and whose singularities are isolated, rational and quasi-homogeneous. We prove then that under a topological hypothesis the obstruction to deforming $X$ concentrates upon its singularities, generalizing partially the results of Namikawa--Gross. We prove also that under a certain hypothesis the locally trivial deformations of $X$ are unobstructed.

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