Unstable Blowups
Algebraic Geometry
2007-11-12 v2 Differential Geometry
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 K\"ahler classes with no constant scalar curvature representatives.
Keywords
Cite
@article{arxiv.math/0702154,
title = {Unstable Blowups},
author = {Jacopo Stoppa},
journal= {arXiv preprint arXiv:math/0702154},
year = {2007}
}
Comments
19 pages. Many improvements. To appear in J. Algebraic Geometry