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math.QA2009★ 20 cited
Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
Domenico Fiorenza, Donatella Iacono, Elena Martinengo
We use the Thom-Whitney construction to show that infinitesimal deformations of a coherent sheaf F are controlled by the differential graded Lie algebra of global sections of an ac…
math.QA2008★ 33 cited
Semicosimplicial DGLAs in deformation theory
Domenico Fiorenza, Marco Manetti, Elena Martinengo
We identify Cech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L-infinity algebra. Applications to deformation theory are described.