Boundedness of regular del Pezzo surfaces over imperfect fields

Hiromu Tanaka

Boundedness of regular del Pezzo surfaces over imperfect fields

Algebraic Geometry 2023-10-26 v4

Authors: Hiromu Tanaka

Abstract

For a regular del Pezzo surface $X$ , we prove that $|-12K_X|$ is very ample. Furthermore, we also give an explicit upper bound for the volume $K_X^2$ which depends only on $[k : k^p]$ for the base field $k$ . As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.

Keywords

del pezzo surfaces algebraic surfaces

Cite

@article{arxiv.1905.00143,
  title  = {Boundedness of regular del Pezzo surfaces over imperfect fields},
  author = {Hiromu Tanaka},
  journal= {arXiv preprint arXiv:1905.00143},
  year   = {2023}
}

Comments

24 pages, v2: minor revisions, v3: minor revisions, v4: minor revisions

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