L-infinity Algebras and Deformations of Holomorphic Maps

Details L-infinity Algebras and Deformations of Holomorphic Maps L-infinity Algebras and Deformations of Holomorphic Maps

2007-05-31

arxiv.org/abs/0705.4532v2

Internat. Math. Res. Notices (2008); Vol. 2008, article ID rnn013, 36 pages

Mathematics

Algebraic Geometry

Revised Version; 26 pages

Scientific paper

We construct the deformation functor associated with a pair of morphisms of
differential graded Lie algebras, and use it to study infinitesimal
deformations of holomorphic maps of compact complex manifolds. In particular,
using L-infinity structures, we give an explicit description of the
differential graded Lie algebra that controls this problem.

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