Abstract
We shall discuss work of the following mathematicians, among others, in this chapter.
Section 19.1 is an introduction to multivariate holomorphic geometry; we shall assume the reader is familiar with the relevant material of Books I and II. Section 19.2 is an introduction to the geometry of complex projective space. In Section 19.3, we discuss Hodge manifolds. Section 19.4 treats the Kodaira Embedding Theorem; we show any compact holomorphic manifold admits a positive line bundle if and only if it embeds as a compact holomorphic submanifold of a complex projective space of some dimension. The elliptic operator theory of Chapter 17 and the analysis of Chapter 18 play a crucial role here.
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Calviño-Louzao, E., García-Río, E., Vázquez-Lorenzo, R., Gilkey, P., Park, J. (2021). Complex Geometry. In: Aspects of Differential Geometry V. Synthesis Lectures on Mathematics & Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-02432-0_4
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DOI: https://doi.org/10.1007/978-3-031-02432-0_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-01304-1
Online ISBN: 978-3-031-02432-0
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