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International Mathematics Research Notices (2000) 2000:147-164, doi:10.1155/S1073792800000106
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

An L{infty}-algebra of an unobstructed deformation functor

S. A. Merkulov

This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on the simple observation that the Kuranishi map can always be inverted in the category of L{infty}-algebras. The L{infty}-structure obtained by this inversion is used to define an unobstructed deformation functor, which is always representable by a smooth pointed moduli space.

The singular nature of the originial Kuranishi deformation space emerges in this setting merely as a result of the truncation of the naive L{infty}-algebra controlling the deformations to a usual differential Lie algebra.


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