Deformations of Compact Calabi--Yau Conifolds

Key Points

Deformations of compact spaces reveal that obstruction focuses specifically on isolated singularities.
Obstruction findings generalize earlier results from Namikawa and Gross, enhancing understanding of deformation theory.
Analysis involves compact normal Kähler spaces with isolated, rational, and quasi-homogeneous singularities.
Research suggests that certain hypotheses enable unobstructed locally trivial deformations in these spaces.

Abstract

Let X be a compact normal Kähler space whose canonical sheaf is a rank-one free OX 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.

Deformations of Compact Calabi--Yau Conifolds

Key Points

Abstract

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