Semiregularity and obstructions of complete intersections

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.

V2 typos corrected, 30 pages. V3 typos and references updated

References in corpus (5)

• Reduced classes and curve counting on surfaces I: theory
• Deformation theory and rational homotopy type
• Lectures on deformations of complex manifolds
• Reduced classes and curve counting on surfaces II: calculations
• Semiregularity as a consequence of Goodwillie's theorem

Cited by in corpus (15)

• Reduced classes and curve counting on surfaces I: theory
• Deformations and obstructions of pairs (X,D)
• Nonabelian higher derived brackets
• Semiregularity as a consequence of Goodwillie's theorem
• Completion and torsion over commutative DG rings
• On deformations of pairs (manifold, coherent sheaf)
• Descent of Deligne-Getzler $\infty$-groupoids
• Obstructions to deforming maps from curves to surfaces
• On coisotropic deformations of holomorphic submanifolds
• $L_{\infty }$ liftings of semiregularity maps via Chern-Simons classes
• Endomorphisms of Koszul complexes: formality and application to deformation theory
• Connections and $L_{\infty }$ liftings of semiregularity maps
• Semiregularity via derived deformation theory
• On the abstract Bogomolov-Tian-Todorov Theorem
• Chern character, semi-regularity map and obstructions