Semiregularity and obstructions of complete intersections

Donatella Iacono, Marco Manetti

Published 2011-12-02, updated 2012-11-09Version 4

We prove that, on a smooth projective variety over an algebraically closed field of characteristic 0, the semiregularity map annihilates every obstruction to embedded deformations of a local complete intersection subvariety with extendable normal bundle. The proof is based on the theory of L-infinity algebras and Tamarkin-Tsigan calculus on the de Rham complex of DG-schemes.