Dolbeault-Massey triple products of low degree
The authors characterize the non-vanishing of special Dolbeault-Massey triple products of low degree in differential bigraded algebras, with applications to the Dolbeault complex of compact complex manifolds. Dolbeault-Massey products are obstructions to Dolbeault formality in the sense of [\textit{J. Neisendorfer} and \textit{L. Taylor}, Trans. Am. Math. Soc. 245, 183--210 (1978; Zbl 0441.55014)]. In particular, the Dolbeault complex of compact complex manifolds satisfying the \(\partial\overline\partial\)-Lemma is Dolbeault formal. The main result is Theorem 3.2, which characterizes when the Dolbeault-Massey triple product \(\left\langle [X], [X], [Y] \right\rangle\) is non-vanishing, where \(X\) is of bidegree \((1,0)\) and \(Y\) is of bidegree \((0,1)\).
scientific article; zbMATH DE number 6508432
scientific article