Connections and L∞ liftings of semiregularity maps

Abstract

Let E⁎ be a finite complex of locally free sheaves on a complex manifold X. We prove that to every connection of type (1,0) on E⁎ it is canonically associated an L∞ morphismg:AX0,⁎(HomOX⁎(E⁎,E⁎))⇝AX⁎,⁎AX≥2,⁎[2] that lifts the 1-component of the Buchweitz-Flenner semiregularity map. An application to deformations of coherent sheaves on projective manifolds is given.