Semiregularity and obstructions of complete intersections

TL;DR

This paper demonstrates that semiregularity maps eliminate obstructions to deforming certain subvarieties on smooth projective varieties, using advanced algebraic techniques.

Contribution

It introduces a new proof showing semiregularity maps nullify obstructions for embedded deformations of local complete intersections with extendable normal bundles.

Findings

Semiregularity map kills all obstructions in the specified setting.

Uses L-infinity algebra and Tamarkin-Tsigan calculus techniques.

Applicable to deformations on smooth projective varieties.

Abstract

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.