On the spectral sequence associated to a multicomplex

Dolbeault cohomology for almost complex manifolds

“…) have a known description, given by Livernet-Whitehouse-Ziegenhagen in [LWZ18]. We obtain: E p+n,−p 0 (A, F ) ∼ = A p,n−p and δ 0 = μ.…”

“…Lastly, the description of E p+n,−p 2 (A, F ) and δ 1 = δ 2 appearing in [LWZ18], directly gives the formulas in the statement of the theorem.…”

“…As explained in Remark 3.7, F is the column filtration on the total complex of a multicomplex (A, d 0 , d 1 , d 2 , d 3 ) with four differentials d i where, due to the shifts in the indices, d 0 = μ has bidegree (−1, 0), d 1 = ∂ has bidegree (0, 1), d 2 = ∂ has bidegree (1, 0) and d 3 = µ has bidegree (2, −1). The spectral sequence of a general multicomplex has been described by Livernet-Whitehouse-Ziegenhagen in [LWZ18] and gives the above equations in the case of a multicomplex with only four components.…”