Endomorphisms of Koszul complexes: formality and application to deformation theory

  • Francesca Carocci
  • Marco ManettiEmail author


We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative \(\mathbb {K}\,\)-algebra R and we prove that it is homotopy abelian over \(\mathbb {K}\,\) 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.


Koszul complex Deformations of coherent sheaves Differential graded Lie algebras 

Mathematics Subject Classification

17B70 14D15 18G50 13D10 



M.M. wishes to acknowledge the support by Italian MIUR under PRIN Project 2015ZWST2C “Moduli spaces and Lie theory”. F.C. thanks the second named author who proposed this project for her master thesis in the far 2014 [2]. F.C. was supported by the Engineering and Physical Sciences Research Council [EP/L015234/1]. The EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London


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Authors and Affiliations

  1. 1.School of Mathematics “James Clerk Maxwell building”University of EdinburghEdinburghUK
  2. 2.Dipartimento di Matematica “Guido Castelnuovo”Università degli studi di Roma “La Sapienza”RomeItaly

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