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

2018/12/17 by Chinburg, T., Guignard, Q., Soulé, C.
#11F11 #14G35 #14G40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.06849

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 SL₂(Z) and to the minimal sup norm of algebraic functions on adelic subsets of curves arising in capacity theory.

Related

• Secant varieties and successive minima
• Linear projections and successive minima
• Distribution of the successive minima of the Petersson norm on cusp forms
• Successive minima of line bundles
• Very stable extensions on arithmetic surfaces