2021/04/26 by Lepri, Emma
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.12658
Given a transitive DG-Lie algebroid (A, ρ) over a smooth separated scheme X of finite type over a field \mathbbK of characteristic 0 we define a notion of connection ∇ \colon RΓ(X,Ker ρ) → RΓ(X,ΩX1[-1]⊗ Ker ρ) and construct an L_∞ morphism between DG-Lie algebras f \colon RΓ(X, Ker ρ) \rightsquigarrowRΓ(X, ΩX≤ 1 [2]) associated to a connection and to a cyclic form on the DG-Lie algebroid. In this way, we obtain a lifting of the first component of the modified Buchweitz-Flenner semiregularity map in the algebraic context, which has an application to the deformation theory of coherent sheaves on X admitting a finite locally free resolution. Another application is to the deformations of (Zariski) principal bundles on X.