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Degeneration of spectral sequences and complex Lagrangian submanifolds (1907.04742v2)
Published 10 Jul 2019 in math.AG, math.QA, and math.RT
Abstract: There is a local-to-global $\mathrm{Ext}$ spectral sequence $\mathrm{E}2{p,q} = \mathrm{H}p(\mathrm{L}, \Omegaq\mathrm{L}) \Rightarrow \mathrm{Ext}{p+q}(i_*\mathscr{O}_\mathrm{L}, i_*\mathscr{O}{\mathrm{L}})$ for a smooth Lagrangian subvariety in a hyperk\"ahler variety. We prove its degeneration on $\mathrm{E}{2}$, and various generalisations thereof.