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arXiv · 1802.07203

Endomorphisms of Koszul complexes: formality and application to deformation theory

Francesca Carocci·Marco Manetti
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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.

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Francesca Carocci, Marco Manetti. 2018-02-20. Endomorphisms of Koszul complexes: formality and application to deformation theory. https://doi.org/10.1007/s12215-018-00394-w

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