Natural operations on holomorphic forms

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Natural operations on holomorphic forms

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Title: Natural operations on holomorphic forms
Author: Navarro Garmendia, Alberto; Navarro Garmendia, José; Tejero Prieto, Tomás Carlos
Abstract: Demostramos que las únicas operaciones diferenciales naturales entre las formas holomórficas en una variedad compleja son las que se obtienen usando combinaciones lineales, el producto exterior y el diferencial exterior. Para llevar a cabo esta tarea, primero desarrollamos los fundamentos de la teoría de los haces holomórficos naturales sobre una variedad fija, haciendo explícita su estructura galoisiana al probar una equivalencia categórica a la Galois.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.
URI: http://hdl.handle.net/10662/10865
Date: 2018


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