English

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