Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1812.06849

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

T. Chinburg·Q. Guignard·C. Soulé
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

T. Chinburg, Q. Guignard, C. Soulé. 2020-01-11. On the slopes of the lattice of sections of Hermitian line bundles. https://arxiv.org/abs/1812.06849

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗