Endomorphisms of Koszul complexes: formality and application to deformation theory

Abstract

We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative $K$-algebra $R$ and we prove that it is homotopy abelian over $K$, while it is generally not formal over $R$. We apply this result to prove an annihilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.

Typos corrected, added section on obstructions to derived deformations. Final version, to appear in "Rend. Circ. Mat. Palermo, II."

References in corpus (4)

• Deformation theory via differential graded Lie algebras
• Lectures on deformations of complex manifolds
• A DG-enhancement of D(QCoh(X)) with applications in deformation theory
• Some remarks on Dupont contraction

Cited by in corpus (1)

• Involutions, obstructions and mirror symmetry