Cosimplicial DGLAs in Deformation Theory

DOI10.1080/00927872.2011.577479zbMath1267.18013arXiv0803.0399OpenAlexW2077137106MaRDI QIDQ2903382

Marco Manetti, Elena Martinengo, Domenico Fiorenza

Publication date: 8 August 2012

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0399

zbMATH Keywords

\(L_\infty\)-algebrasMaurer Cartan elementsCech cocycleDeligne functor

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Graded Lie (super)algebras (17B70) Deformations and infinitesimal methods in commutative ring theory (13D10)

Related Items (15)

Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves ⋮ Cyclic forms on DG-Lie algebroids and semiregularity ⋮ The logarithmic Bogomolov–Tian–Todorov theorem ⋮ Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex ⋮ Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties ⋮ Posetted trees and Baker-Campbell-Hausdorff product ⋮ Deformations of polystable sheaves on surfaces: quadraticity implies formality ⋮ Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle) ⋮ On the Lie algebroid of a derived self-intersection ⋮ On Deformations of Pairs (Manifold, Coherent Sheaf) ⋮ Some remarks on Dupont contraction ⋮ Connections and \(L_\infty\) liftings of semiregularity maps ⋮ Log smooth deformation theory via Gerstenhaber algebras ⋮ Smoothing toroidal crossing spaces ⋮ Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds

Cites Work

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• Small models for chain algebras
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• Deformation quantization of Poisson manifolds
• Lie theory for nilpotent \(L_{\infty}\)-algebras
• Deformations of sheaves of algebras
• Deformations of Algebraic Schemes
• Descent of Deligne groupoids
• Simplicial homotopy theory
• DG coalgebras as formal stacks

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