Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts

DOI10.4171/PRIMS/57-3-13arXiv1701.02840MaRDI QIDQ6281779

Kenji Fukaya

Publication date: 10 January 2017

Abstract: In this paper we give detailed construction of $G$-equivariant Kuranishi chart of moduli spaces of pseudo-holomorphic curves to a symplectic manifold with $G$-action, for an arbitrary compact Lie group $G$. The proof is based on the deformation theory of {it unstable} marked curves using the language of Lie groupoid (which is {it not} necessary etale) and the Riemannnian center of mass technique. This proof is actually similar to [FOn,Sections 13 and 15] except the usage of the language of Lie groupoid makes the argument more transparent. This version correct some errors of the previous version especially those pointed out by the referee.

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