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On subfiniteness of graded linear series

  • Huayi ChenEmail author
  • Hideaki Ikoma
Research Article
  • 12 Downloads

Abstract

Hilbert’s fourteenth problem studies the finite generation property of the intersection of an integral algebra of finite type with a subfield of the fraction field of the algebra. It has a negative answer due to a counterexample of Nagata. We show that a subfinite version of Hilbert’s fourteenth problem has an affirmative answer. We then establish a graded analogue of this result, which permits to show that the subfiniteness of graded linear series does not depend on the function field in which we consider it. Finally, we apply the subfiniteness result to the study of geometric and arithmetic graded linear series.

Keywords

Hilberts fourteenth problem Algebra of subfinite type Graded linear series Newton–Okounkov bodies 

Mathematics Subject Classification

14G40 11G30 

Notes

Acknowledgements

Huayi Chen would like to thank the Beijing International Center for Mathematical Research for their hospitality and support of his visiting position. We are grateful to Kiumars Kaveh for communications and comments. We are also grateful to anonymous referees for their suggestions and comments.

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Copyright information

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Authors and Affiliations

  1. 1.Université Paris Diderot, Sorbonne Université, CNRS, Institut de Mathématiques de Jussieu- Paris Rive Gauche, IMJ-PRGParisFrance
  2. 2.Faculty of EducationShitennoji UniversityHabikinoJapan

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