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Igor Khavkine
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A supermanifold is a graded manifold with only odd components, more precisely the equivalence is seen by setting $V_{\bar{0}}=0$ and $V_{\bar{1}} = V$ in your notation. In the opposite direction, a graded manifold is a supermanifold only if it has no even components, that is $V_{\bar{0}} = 0$.

Igor Khavkine
  • 21.5k
  • 2
  • 60
  • 113