Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Boundedness of the successive minima on arithmetic varieties


Author: Hideaki Ikoma
Journal: J. Algebraic Geom. 22 (2013), 249-302
DOI: https://doi.org/10.1090/S1056-3911-2012-00600-6
Published electronically: July 10, 2012
MathSciNet review: 3019450
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Abstract | References | Additional Information

Abstract: In this paper, we study the asymptotic behavior of the successive minima associated with high powers of a Hermitian invertible sheaf on an arithmetic variety. As a consequence, we prove that the arithmetic $ \hat {\chi }$-volume function, which is introduced by Yuan, is homogeneous, birationally invariant, and continuous on the arithmetic Picard group. We also obtain the arithmetic Hilbert-Samuel formula for vertically nef Hermitian invertible sheaves.


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Additional Information

Hideaki Ikoma
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan
Email: ikoma@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S1056-3911-2012-00600-6
Received by editor(s): May 27, 2010
Received by editor(s) in revised form: May 4, 2011
Published electronically: July 10, 2012
Dedicated: Dedicated to the memory of Professor Masaki Maruyama.

American Mathematical Society