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 but not over R (except trivial cases). We apply this result to prove an anni hilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.
Carocci, F., Manetti, M. (2020). Endomorphisms of Koszul complexes: formality and application to deformation theory. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 69(1), 175-193 [10.1007/s12215-018-00394-w].
Endomorphisms of Koszul complexes: formality and application to deformation theory
Carocci F;
2020-01-01
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 but not over R (except trivial cases). We apply this result to prove an anni hilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.File in questo prodotto:
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