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A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles

Ben Weinkove
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Abstract

This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the destabilizing sheaf satisfies a differential inclusion relation. This relation is used, together with a complex Frobenius theorem for locally finitely generated subsheaves, to imply coherence of the destabilizing subsheaf.

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Ben Weinkove. 2003-08-01. A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles. https://arxiv.org/abs/math/0306073

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