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We consider deformations over non-commutative base space instead of the usual commutative base. Then there are more deformations which give more information. NC deformation theory works for sheaves on varieties as well as varieties themselves. NC deformations of flopping curves on 3-folds considered by Donovan-Wemyss give Gopakumar-Vafa invariants. NC deformations on surfaces with quotient singularities give Hacking’s vector bundles under Koll\’ar-Shepherd-Barron’s Q-Gorenstein smoothing.