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arXiv · 1311.0410

The moment-weight inequality and the Hilbert-Mumford criterion

Valentina Georgoulas·Joel W. Robbin·Dietmar A. Salamon
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Abstract

This paper gives an essentially self-contained exposition (except for an appeal to the Lojasiewicz gradient inequality) of geometric invariant theory from a differential geometric viewpoint. Central ingredients are the moment-weight inequality (relating the Mumford numerical invariants to the norm of the moment map), the negative gradient flow of the moment map squared, and the Kempf-Ness function.

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Valentina Georgoulas, Joel W. Robbin, Dietmar A. Salamon. 2013-11-02. The moment-weight inequality and the Hilbert-Mumford criterion. https://arxiv.org/abs/1311.0410

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