Forms of del Pezzo surfaces of degree 5 and 6

Alexandr Zaitsev

Forms of del Pezzo surfaces of degree 5 and 6

Algebraic Geometry 2024-02-06 v1

Authors: Alexandr Zaitsev

Abstract

In this paper we obtain necessary and sufficient condition for existence of del Pezzo surfaces of degree $5$ and $6$ over a field $K$ with a prescribed action of absolute Galois group $\text{Gal} ( K^{\text{sep}}/K)$ on the graph of $(-1)$ -curves. Also we compute automorphism groups of del Pezzo surfaces of degree $5$ over arbitrary fields.

Keywords

del Pezzo surfaces degree 5 degree 6 absolute Galois group (-1)-curves automorphism groups

Cite

@article{arxiv.2302.04937,
  title  = {Forms of del Pezzo surfaces of degree 5 and 6},
  author = {Alexandr Zaitsev},
  journal= {arXiv preprint arXiv:2302.04937},
  year   = {2024}
}

Comments

14 pages, 1 figure, 1 table

Related papers

View all related →