Proposition 4.8 . [051Z] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Proposition 4.8 .
There is a holomorphic embedding Φ : ( ℳ , Ω ) → 𝒩 0 \Phi:(\mathcal{M},\Omega)\rightarrow\mathcal{N}^{0} 𝒫 \mathcal{P}
(1)
Φ \Phi commutes with the projection maps to D D .
(2)
Φ ∗ Ω 𝒩 0 = Ω . \Phi^{*}\Omega_{\mathcal{N}^{0}}=\Omega.
(3)
d Φ ( ξ 1 , 0 ) = ξ 𝒩 0 1 , 0 d\Phi(\xi^{1,0})=\xi^{1,0}_{\mathcal{N}^{0}} . In particular, Φ \Phi maps 𝒫 \mathcal{P} isomorphically onto ℋ \mathcal{H} .