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- W2037345707 abstract "In this paper, we explore holomorphic Segre preserving maps. First, we investigate holomorphic Segre preserving maps sending the complexification $mathcal{M}$ of a generic real analytic submanifold $M subseteq C^N$ of finite type at some point $p$ into the complexification $mathcal{M}'$ of a generic real analytic submanifold $M' subseteq C^{N'}$, finitely nondegenerate at some point $p'$. We prove that for a fixed $M$ and $M'$, the germs at $(p,bar{p})$ of Segre submersive holomorphic Segre preserving maps sending $(M,(p,bar{p}))$ into $(M',(p', bar{p}'))$ can be parametrized by their $r$-jets at $(p,bar{p})$, for some fixed $r$ depending only on $M$ and $M'$. (If, in addition, $M$ and $M'$ are both real algebraic, then we prove that any such map must be holomorphic algebraic.) From this parametrization, it follows that the set of germs of holomorphic Segre preserving automorphisms $mathcal{H}$ of the complexification $mathcal{M}$ of a real analytic submanifold finitely nondegenerate and of finite type at some point $p$, and such that $mathcal{H}$ fixes $(p,bar{p})$, is an algebraic complex Lie group. We then explore the relationship between this automorphism group and the group of automorphisms of $M$ at $p$." @default.
- W2037345707 created "2016-06-24" @default.
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- W2037345707 date "2010-08-11" @default.
- W2037345707 modified "2023-10-18" @default.
- W2037345707 title "Parametrization of holomorphic Segre-preserving maps" @default.
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- W2037345707 doi "https://doi.org/10.2140/pjm.2010.247.283" @default.
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