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Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension 2.

Masahide Kato — 1976

Mathematische Annalen

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato; Noboru Okada — 2004

Annales de l’institut Fourier

We study the extension problem of holomorphic maps $σ : H \to X$ of a Hartogs domain $H$ with values in a complex manifold $X$ . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain $Ω_{σ}$ of extension for $σ$ over $Δ$ is contained in a subdomain of $Δ$ . For such manifolds, we define, in this paper, an invariant Hex $_{n} (X)$ using the Hausdorff dimensions of the singular sets of $σ$ ’s and study its properties to deduce informations on the complex structure of $X$ .

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