Birational classification of pointless del Pezzo surfaces of degree 8

Andrey Trepalin

Birational classification of pointless del Pezzo surfaces of degree 8

Algebraic Geometry 2022-10-20 v3

Authors: Andrey Trepalin

Abstract

Let k be a perfect field. Recently J.-L. Colliot-Th\'el\`ene showed that two pointless quadric surfaces over k are birationally equivalent if and only if they are isomorphic. We show that this result holds for arbitrary del Pezzo surfaces of degree $8$ with the Picard number $1$ , and describe minimal surfaces birationally equivalent to a given pointless del Pezzo surface of degree $8$ .

Keywords

del pezzo surfaces birational equivalence pointless varieties perfect field picard number quadric surfaces minimal surfaces

Cite

@article{arxiv.2202.11030,
  title  = {Birational classification of pointless del Pezzo surfaces of degree 8},
  author = {Andrey Trepalin},
  journal= {arXiv preprint arXiv:2202.11030},
  year   = {2022}
}

Comments

3-rd version. Some results are improved. In particular, the main result holds for arbitrary perfect field k. 19 pages, 1 table

Birational classification of pointless del Pezzo surfaces of degree 8

Abstract

Keywords

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