Localizing the Donaldson-Futaki invariant

Eveline Legendre

Localizing the Donaldson-Futaki invariant

Differential Geometry 2020-06-17 v1

Authors: Eveline Legendre

Abstract

We use the equivariant localization formula to prove that the Donaldson-Futaki invariant of a compact smooth (K{\"a}hler) test configuration coincides with the Futaki invariant of the induced action on the central fiber when this fiber is smooth or have orbifold singularities. We also localize the Donaldson-Futaki invariant of the deformation to the normal cone.

Keywords

donaldson-thomas invariants

Cite

@article{arxiv.2006.08987,
  title  = {Localizing the Donaldson-Futaki invariant},
  author = {Eveline Legendre},
  journal= {arXiv preprint arXiv:2006.08987},
  year   = {2020}
}