English

On local delta invariant of del Pezzo surfaces

Algebraic Geometry 2024-08-12 v2

Abstract

We complete the classification of local stability thresholds for smooth del Pezzo surfaces of degree~2. In particular, we show that this number is irrational if and only if a unique (-1)-curve passes through the point where we are computing the local invariant.

Keywords

Cite

@article{arxiv.2304.12286,
  title  = {On local delta invariant of del Pezzo surfaces},
  author = {Erroxe Etxabarri Alberdi},
  journal= {arXiv preprint arXiv:2304.12286},
  year   = {2024}
}

Comments

We generalize the result of the previous version, proving that for any point in a del Pezzo surface of degree 2 contained in a unique (-1)-curve the local stability threshold is irrational