Connections and L∞ liftings of semiregularity maps

Let epsilon* be a finite complex of locally free sheaves on a complex manifold X. We prove that to every connection of type (1, 0) on epsilon* it is canonically associated an L-infinity morphism g: A(X)(0,)* (Hom(Ox)* (epsilon*, epsilon*)) -> A(X)*(,)*/A(X)(>= 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. (C) 2021 Elsevier B.V. All rights reserved.