Displaying similar documents to “Extension of line bundles and holomorphic maps”

An extension of Schwick's theorem for normal families

Yasheng Ye, Xuecheng Pang, Liu Yang (2015)

Annales Polonici Mathematici

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In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.

Natural operations on holomorphic forms

A. Navarro, J. Navarro, C. Tejero Prieto (2018)

Archivum Mathematicum

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We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.