Degeneration of spectral sequences and complex Lagrangian submanifolds

Abstract

There is a local-to-global $\mathrm{Ext}$ spectral sequence ${\mathrm{E}}_2^{p,q}={\mathrm{H}}^p(\mathrm{L},{\Omega }_{\mathrm{L}}^q)\Rightarrow {\mathrm{Ext}}^{p+q}(i_{\ast }{\mathcal{O}}_{\mathrm{L}},i_{\ast }{\mathcal{O}}_{\mathrm{L}})$ for a smooth Lagrangian subvariety in a hyperkähler variety. We prove its degeneration on ${\mathrm{E}}_2$, and various generalisations thereof.

comments welcome, deformation quantisation material now in a separate article

References in corpus (2)

• Formality of differential graded algebras and complex Lagrangian submanifolds
• Derived geometry of the first formal neighborhood of a smooth analytic cycle

Cited by in corpus (1)

• Formality of differential graded algebras and complex Lagrangian submanifolds