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arXiv · 1905.11334

K-semistability of optimal degenerations

Ruadhaí Dervan
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Abstract

K-polystability of a polarised variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature K\"ahler metric. When a variety is K-unstable, it is expected to admit a "most destabilising" degeneration. In this note we show that if such a degeneration exists, then the limiting scheme is itself relatively K-semistable.

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Ruadhaí Dervan. 2019-05-27. K-semistability of optimal degenerations. https://arxiv.org/abs/1905.11334

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