Unstable Blowups
Abstract
Description
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.
19 pages. Many improvements. To appear in J. Algebraic Geometry
19 pages. Many improvements. To appear in J. Algebraic Geometry