Delta-invariant for projective bundles over a curve and K-semistability

Houari Benammar Ammar; Louis Massonnet; Chenxi Yin

Delta-invariant for projective bundles over a curve and K-semistability

Algebraic Geometry 2024-11-12 v1

Authors: Houari Benammar Ammar , Louis Massonnet , Chenxi Yin

Abstract

Consider $E$ a vector bundle over a smooth curve $C$ . We compute the $\delta$ -invariant of all ample ( $\mathbb{Q}$ -) line bundles on $\mathbb{P}(E)$ when $E$ is strictly Mumford semistable. We also investigate the case when one assumes that the Harder-Narasimhan filtration of $E$ has only one step.

Keywords

delta-invariant projective bundles K-semistability vector bundles Mumford semistable Harder-Narasimhan filtration ample line bundles algebraic geometry

Cite

@article{arxiv.2411.05976,
  title  = {Delta-invariant for projective bundles over a curve and K-semistability},
  author = {Houari Benammar Ammar and Louis Massonnet and Chenxi Yin},
  journal= {arXiv preprint arXiv:2411.05976},
  year   = {2024}
}

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