$E_1$-degeneration and $d^{\prime }{d}^{\prime \prime }$-lemma

Abstract

For a double complex $(A,d^{\prime },d^{\prime \prime })$, we show that if it satisfies the $d^{\prime }{d}^{\prime \prime }$-lemma and the spectral sequence $\{E_r^{p,q}\}$ induced by $A$ does not degenerate at $E_0$, then it degenerates at $E_1$. We apply this result to prove the degeneration at $E_1$ of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of $d^{\prime }{d}^{\prime \prime }$-lemma.

References in corpus (2)

• New aspects of the ddc-lemma
• Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d^{\prime }{d}^{\prime \prime }$-lemma