Complex lagrangian submanifolds in holomorphic Symplectic varieties and differential graded algebras

We present applications of deformation quantisation techniques to holomorphic symplectic geometry. In particular, we calculate certain Ext groups between quantisable Lagrangian D-branes, which count the massless open strings connecting the D-branes, and show the corresponding RHom DG-algebras are formal. Auxiliary results on A-inf modules over graded algebras are presented as well.Open Acces