不完全域上正则del Pezzo曲面的有界性

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

Hiromu Tanaka

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引用次数: 5

摘要

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。

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Boundedness of regular del Pezzo surfaces over imperfect fields

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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