We study deformations of certain crepant resolutions of isolated rational Gorenstein singularities. After a general discussion of the deformation theory, we specialize to dimension $3$ and consider examples which are good (log) resolutions as well as the case of small resolutions. We obtain some partial results on the classification of canonical threefold singularities that admit good crepant resolutions. Finally, we study a noncrepant example, the blowup of a small resolution whose exceptional set is a smooth curve.

Comment: 35 pages, 3 figures; v6 - final version

• 14B07 - Deformations of singularities
• 14E15 - Global theory and resolution of singularities (algebro-geometric aspects)
• 14J32 - Calabi-Yau manifolds (algebro-geometric aspects)
• 32S30 - Deformations of complex singularities; vanishing cycles
• 32S45 - Modifications; resolution of singularities (complex-analytic aspects)