Endomorphisms of Koszul complexes: formality and application to deformation theory

摘要

We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative Kdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$mathbb {K},$$end{document}-algebra R and we prove that it is homotopy abelian over Kdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$mathbb {K},$$end{document} but not over R (except trivial cases). We apply this result to prove an annihilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.