Related papers: Heights for line bundles on arithmetic surfaces

We consider heights of horizontal irreducible divisors on an arithmetic surface with respect to some hermitian line bundle. We obtain both lower and upper bounds for these heights. The results are different and sometimes stronger that those…

In this book, we establish a theory of adelic line bundles over quasi-projective varieties over finitely generated fields. Besides definitions of adelic line bundles, we consider their intersection theory, volume theory, and height theory,…

By using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic…

We investigate analytic properties of height zeta functions of toric bundles over flag varieties.

For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height on the Jacobian of a smooth projective curve can be computed…

The Griffiths height of a variation of Hodge structures over a projective curve is defined as the degree of its canonical line bundle, as defined by Griffiths and generalized by Peters to allow bad reduction points. It may be seen as a…

We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems…

We investigate analytic properties of height zeta functions of toric varieties. Using the height zeta functions, we prove an asymptotic formula for the number of rational points of bounded height with respect to an arbitrary line bundle…

We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.

We consider the following question: for which invariants $g$ and $e$ is there a geometrically ruled surface $S \rightarrow C$ over a curve $C$ of genus $g$ with invariant $e$ such that $S$ is the support of an Ulrich line bundle with…

Using linear projections one gets new inequalities for the successive minima of the lattice of sections of an hermitian line bundle on an arithmetic surface.

We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…

The purpose of this paper is to give a linear and effective height inequality for algebraic points on curves over functional fields. Our height inequality can be viewed as the logarithmic canonical class inequality of a punctured curve over…

It is known for linear operators with polynomial coefficients annihilating a given D-finite function that there is a trade-off between order and degree. Raising the order may give room for lowering the degree. The relationship between order…

We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors.…

We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…

This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add…

We introduce a new approach to study height zeta functions of projective spaces and projective bundles. To study height zeta functions of projective spaces $Z(\mathbb{P}^n, H_{\mathcal{O}(1)}; s)$, we apply the Riemann-Roch theorem of…

We use constructions of surfaces as abelian covers to write down exceptional collections of line bundles of maximal length for every surface $X$ in certain families of surfaces of general type with $p_g=0$ and $K_X^2=3,4,5,6,8$. We also…

We define various height functions for motives over number fields. We compare these height functions with classical height functions on algebraic varieties, and also with analogous height functions for variations of Hodge structures on…