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 annihilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.
Endomorphisms of Koszul complexes: formality and application to deformation theory / Carocci, F.; Manetti, M.. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 69:1(2020), pp. 175-193. [10.1007/s12215-018-00394-w]
Endomorphisms of Koszul complexes: formality and application to deformation theory
Manetti M.
2020
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 annihilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes.| File | Dimensione | Formato | |
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Carocci_Endomorphisms-of-Koszul_2020.pdf
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Carocci_Endomorphisms-of-Kpszul_2020.pdf
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Note: https://arxiv.org/abs/1802.07203
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