[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）13 (1002ﾚｽ)

純粋・応用数学・数学隣接分野（含むガロア理論）13 http://rio2016.5ch.net/test/read.cgi/math/1674527723/

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956: １３２人目の素数さん [] 2023/07/31(月) 09:13:58.31 ID:jznoxopE This is a continuation of [Oh-5] where the following was proved among other things. Theorem 1.1. Let M be a complex manifold and let Ω be a proper bounded domain in M with C^2-smooth pseudoconvex boundary ∂Ω. Assume that M admits a K¨ahler metric and the canonical bundle K_M of M admits a fiber metric whose curvature form is negative on a neighborhood of ∂Ω. Then there exists a holomorphic map with connected fibers from Ω to C^N for some N ∈ ℕ which is proper onto the image. The main purpose of the present article is to strengthen it by removing the K¨ahlerness assumption (see §2). For that, the proof of Theorem　0.1 given in [Oh-5] by an application of the L^2 vanishing theorem on complete K¨ahler manifolds will be replaced by an argument which is more involved but also seems to be basic (see §1). http://rio2016.5ch.net/test/read.cgi/math/1674527723/956

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