English

Positivity in convergence of the inverse $\sigma_{n-1}$-flow

Differential Geometry 2016-11-01 v1 Algebraic Geometry

Abstract

We study positivity in the conjecture proposed by Lejmi and Sz\'{e}kelyhidi on finding effective necessary and sufficient conditions for solvability of the inverse σk\sigma_k equation, or equivalently, for convergence of the inverse σk\sigma_k-flow. In particular, for the inverse σn1\sigma_{n-1}-flow we partially verify their conjecture by obtaining the desired positivity for (n1,n1)(n-1, n-1) cohomology classes. As an application, we also partially verify their conjecture for 3-folds.

Keywords

Cite

@article{arxiv.1610.09584,
  title  = {Positivity in convergence of the inverse $\sigma_{n-1}$-flow},
  author = {Jian Xiao},
  journal= {arXiv preprint arXiv:1610.09584},
  year   = {2016}
}