Unstable Blowups

Details Unstable Blowups Unstable Blowups

2007-02-06

arxiv.org/abs/math/0702154v2

Mathematics

Algebraic Geometry

19 pages. Many improvements. To appear in J. Algebraic Geometry

Scientific paper

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 K\"ahler classes with no constant scalar curvature representatives.

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