Skip to Main Content
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
Published electronically: July 10, 2012
MathSciNet review: 3019450
Full-text PDF

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.

References [Enhancements On Off] (What's this?)


Additional Information

Hideaki Ikoma
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan

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.