On pairs, triples and quadruples of points on a cubic surface

Sergey Galkin; Pavel Popov

On pairs, triples and quadruples of points on a cubic surface

Algebraic Geometry 2019-04-23 v3 Number Theory

Authors: Sergey Galkin , Pavel Popov

Abstract

Let $X^{(n)}$ denote $n$ -th symmetric power of a cubic surface $X$ . We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$ , despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$ .

Keywords

cubic surface symmetric power stable birationality points on surface

Cite

@article{arxiv.1810.07001,
  title  = {On pairs, triples and quadruples of points on a cubic surface},
  author = {Sergey Galkin and Pavel Popov},
  journal= {arXiv preprint arXiv:1810.07001},
  year   = {2019}
}

Comments

English and Russian versions, 2 pages each. v1: Article in Russian, v2: English translation, v3: added Afterword on page 2 (only in English). Comments welcome!

On pairs, triples and quadruples of points on a cubic surface

Abstract

Keywords

Cite

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