Degeneration of spectral sequences and complex Lagrangian submanifolds

Abstract: There is a local-to-global $\mathrm{Ext}$ spectral sequence $\mathrm{E}2^{p,q} = \mathrm{H}^p(\mathrm{L}, \Omega^q\mathrm{L}) \Rightarrow \mathrm{Ext}^{p+q}(i_*\mathscr{O}_\mathrm{L}, i_*\mathscr{O}{\mathrm{L}})$ for a smooth Lagrangian subvariety in a hyperk\"ahler variety. We prove its degeneration on $\mathrm{E}{2}$, and various generalisations thereof.