Slope inequalities for KSB-stable and K-stable families
Algebraic Geometry
2023-07-17 v2
Abstract
We prove some higher dimensional generalizations of the slope inequality originally due to G. Xiao, and to M. Cornalba and J. Harris. We give applications to families of KSB-stable and K-stable pairs, as well as to the study of the ample cone of the moduli space of KSB-stable varieties. Our proofs relies on the study of the Harder-Narasimhan filtration, and some generalizations of Castelnuovo's and Noether's inequalities.
Keywords
Cite
@article{arxiv.2107.09553,
title = {Slope inequalities for KSB-stable and K-stable families},
author = {Giulio Codogni and Luca Tasin and Filippo Viviani},
journal= {arXiv preprint arXiv:2107.09553},
year = {2023}
}
Comments
To appear in the Proceedings of the London Mathematical Society