$\delta$-invariants of log Fano planes

Elena Denisova

$\delta$-invariants of log Fano planes

Algebraic Geometry 2025-05-29 v1

Authors: Elena Denisova

Abstract

We compute the $\delta$ -invariant for pairs $(\mathbb{P}^2, \lambda C_d)$ , where $C_d$ is a plane curve of degree $d \leq 4$ . These computations provide new examples of $K$ -stable and $K$ -semistable log Fano pairs, and contribute to the study of $K$ -stability of log Fano varieties via the Abban-Zhuang method, which reduces higher-dimensional problems to the surface case.

Keywords

$\delta$-invariant log Fano pairs $K$-stability plane curve Abban-Zhuang method

Cite

@article{arxiv.2505.22528,
  title  = {$\delta$-invariants of log Fano planes},
  author = {Elena Denisova},
  journal= {arXiv preprint arXiv:2505.22528},
  year   = {2025}
}

Comments

70 pp

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