Hodge spectral sequence and symmetry on compact Kähler spaces (Q1097376)

Let X be a compact Kähler space of pure dimension, and \(Y\subset X\) a complex subspace such that (X\(\setminus Y)\) is smooth. It is proved that the Hodge spectral sequence on (X\(\setminus Y)\) degenerates at its \(E_ 1\)-term \((:=Ker {\bar \partial}/Im {\bar \partial})\) in degrees less than \(((co\dim Y)-1);\) moreover, if \(p+q\leq ((co\dim Y)-2)\) then: \(E_ 1^{p,q}(X\setminus Y)\cong E_ 1^{q,p}(X\setminus Y).\) The proof uses an L 2-version of Andreotti-Grauert's vanishing theorem on q-complete spaces, as well as Andreotti-Vesentini's theorem.