1999/07/14 by S. A. Merkulov
Mathematics · #math.AG
published as Intern. Math. Research Notices 3 (2000) 147-164 · LaTeX, 15 pages; small changes
arxiv created 1999/07/14 · arxiv updated 2009/11/30
This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on a simple observation that the Kuranishi map can always be inverted in the category of L∞-algebras. The L∞-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 original Kuranishi deformation space emerges in this setting merely as a result of the truncation of this ``naive'' L∞-algebra controlling the deformations to a usual differential Lie algebra.