Log-pluricanonical forms on nondegenerate hypersurfaces extend to 1-parameter deformations, yielding simultaneous log-canonical models under equisingular conditions.
This description shows that they are extendable to 1- parameter deformations
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A remark on extension of log-pluricanononical forms for nondegenerate hypersurfaces
Log-pluricanonical forms on nondegenerate hypersurfaces extend to 1-parameter deformations, yielding simultaneous log-canonical models under equisingular conditions.