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Unstable Blowups

Jacopo Stoppa
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Abstract

Let (X,L) be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of X along a 0-dimensional cycle are closely related to Chow stability of the cycle itself, for polarizations making the exceptional divisors small. This can be used to give (almost) a converse to a result of Arezzo and Pacard, and to give new examples of Kähler classes with no constant scalar curvature representatives.

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Jacopo Stoppa. 2007-11-12. Unstable Blowups. https://arxiv.org/abs/math/0702154

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