$L_{\infty}$-algebra of an unobstructed deformation functor

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dc.creatorMerkulov, S. A.
dc.date1999-07-06
dc.date1999-07-14
dc.date.accessioned2026-07-07T05:29:47Z
dc.date.available2026-07-07T05:29:47Z
dc.descriptionThis 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 $L_{\infty}$-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 original Kuranishi deformation space emerges in this setting merely as a result of the truncation of this ``naive'' $L_{\infty}$-algebra controlling the deformations to a usual differential Lie algebra.
dc.descriptionLaTeX, 15 pages; small changes
dc.identifierhttps://arxiv.org/abs/math/9907031
dc.identifierhttp://arxiv.org/abs/math/9907031
dc.identifierIntern. Math. Research Notices 3 (2000) 147-164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78778
dc.subjectAlgebraic Geometry
dc.title$L_{\infty}$-algebra of an unobstructed deformation functor
dc.typetext

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