Serre duality for projective supermanifolds (Q1057555)

The article deals with the extension of the Serre duality theorem to projective supermanifolds. It turns out that the dualizing bundle to a given supermanifold X is Ber X; this conjecture was expressed by P. Deligne in an unpublished paper earlier. In particular, the canonical isomorphism \(H^ i(X,\Omega^ kX)=H^{n-i}(X,\Sigma_{n-m-k}X)^*\) is true for a projective supermanifold X. The main result lets stand the invariant definition of Berezinian Ber X.