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Mathematics > Algebraic Geometry

arXiv:1812.06849 (math)
[Submitted on 17 Dec 2018 (v1), last revised 11 Jan 2020 (this version, v2)]

Title:On the slopes of the lattice of sections of Hermitian line bundles

Authors:T. Chinburg, Q. Guignard, C. Soulé
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Abstract:In this paper we study the distribution of successive minima of global sections of powers of a metrized ample line bundle on a variety over a number field. We develop criteria for there to exist a measure on the real line describing the limiting behavior of this distribution as one considers increasing powers of the bundle. When this measure exists, we develop methods for determining it explicitly. We present applications to the distribution of Petersson norms of cusp forms of increasing weight for SL_2(Z) and to the minimal sup norm of algebraic functions on adelic subsets of curves arising in capacity theory.
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14G40, 14G35, 11F11
Cite as: arXiv:1812.06849 [math.AG]
  (or arXiv:1812.06849v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.06849

Submission history

From: Ted Chinburg [view email]
[v1] Mon, 17 Dec 2018 15:47:58 UTC (53 KB)
[v2] Sat, 11 Jan 2020 12:03:37 UTC (54 KB)
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