Boundedness of regular del Pezzo surfaces over imperfect fields

For a regular del Pezzo surface X , we prove that | - 12 K 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 surfac...

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Bibliographic Details
Published inManuscripta mathematica Vol. 174; no. 1-2; pp. 355 - 379
Main Author Tanaka, Hiromu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2024
Springer Nature B.V
Subjects
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
Upper bounds
14D06
14G17
Online AccessGet full text
ISSN0025-2611
1432-1785
DOI10.1007/s00229-023-01517-z

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Summary:For a regular del Pezzo surface X , we prove that | - 12 K 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-023-01517-z