Boundedness of regular del Pezzo surfaces over imperfect fields

IF 0.5 4区数学 Q3 MATHEMATICS

Manuscripta Mathematica Pub Date : 2023-10-30 DOI:10.1007/s00229-023-01517-z

Hiromu Tanaka

引用次数: 5

Abstract

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

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不完全域上正则del Pezzo曲面的有界性

摘要对于正则del Pezzo曲面X，证明了$$|-12K_X|$$ | - 12 K X |是非常充足的。此外，我们还给出了体积$$K_X^2$$ K x2的显式上界，该上界仅取决于基础场K的$$[k: k^p]$$ [K: kp]。由此得到几何积分正则del Pezzo曲面的有界性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Manuscripta Mathematica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.