15 citations · 56 across the 25 of their papers we have counts for
22 papers · 1 filter
Rings of tautological forms on moduli spaces of curves
Robin de Jong, Stefan van der Lugt
We define and study a natural system of tautological rings on the moduli spaces of marked curves at the level of differential forms. We show that certain 2-forms obtained from the…
Heights on curves and limits of Hodge structures
Spencer Bloch, Robin de Jong, Emre Can Sertöz
We exhibit a precise connection between Néron--Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singula…
Frobenius' theta function and Arakelov invariants in genus three
Robin de Jong
We give explicit formulas for the Kawazumi-Zhang invariant and Faltings delta-invariant of a compact and connected Riemann surface of genus three. The formulas are in terms of two…
Tropical moments of tropical Jacobians
Robin de Jong, Farbod Shokrieh
Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant associated to each polarized real torus…
Faltings height and Néron-Tate height of a theta divisor
Robin de Jong, Farbod Shokrieh
We prove a formula, which, given a principally polarized abelian variety over the field of algebraic numbers, relates the stable Faltings height of with the Néron--Tate…
Chern-Weil theory for line bundles with the family Arakelov metric
Michiel Jespers, Robin de Jong
We prove a result of Chern-Weil type for canonically metrized line bundles on one-parameter families of smooth complex curves. Our result generalizes a result due to J.I. Burgos Gi…
Singularities of the biextension metric for families of abelian varieties
Jose Ignacio Burgos Gil, David Holmes, Robin de Jong
In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an…
Point-like limit of the hyperelliptic Zhang-Kawazumi invariant
Robin de Jong
The behavior near the boundary in the Deligne-Mumford compactification of many functions on the moduli space of pointed Riemann surfaces can be conveniently expressed using the not…
Faltings delta-invariant and semistable degeneration
Robin de Jong
We determine the asymptotic behavior of the Arakelov metric, the Arakelov-Green's function, and the Faltings delta-invariant for arbitrary one-parameter families of complex curves…
Néron models and the height jump divisor
Owen Biesel, David Holmes, Robin de Jong
We define an algebraic analogue, in the case of jacobians of curves, of the height jump divisor introduced recently by R. Hain. We give explicit combinatorial formulae for the heig…
Asymptotics of the Néron height pairing
David Holmes, Robin de Jong
The aim of this paper is twofold. First, we study the asymptotics of the Néron height pairing between degree-zero divisors on a family of degenerating compact Riemann surfaces para…
Normal functions and the height of Gross-Schoen cycles
Robin de Jong
We prove a variant of a formula due to S. Zhang relating the Beilinson-Bloch height of the Gross-Schoen cycle on a pointed curve with the self-intersection of its relative dualizin…
Special values of canonical Green's functions
Robin de Jong
We give a precise formula for the value of the canonical Green's function at a pair of Weierstrass points on a hyperelliptic Riemann surface. Further we express the 'energy' of the…
Asymptotic behavior of the Kawazumi-Zhang invariant for degenerating Riemann surfaces
Robin de Jong
Around 2008 N. Kawazumi and S. Zhang introduced a new fundamental numerical invariant for compact Riemann surfaces. One way of viewing the Kawazumi-Zhang invariant is as a quotient…
Second variation of Zhang's lambda-invariant on the moduli space of curves
Robin de Jong
We compute the second variation of the λ-invariant, recently introduced by S. Zhang, on the complex moduli space M_g of curves of genus g>1, using work of N. Kawazumi. As a result…
Symmetric roots and admissible pairing
Robin de Jong
Using the discriminant modular form and the Noether formula it is possible to write the admissible self-intersection of the relative dualising sheaf of a semistable hyperelliptic c…
Admissible constants for genus 2 curves
Robin de Jong
S.-W. Zhang recently introduced a new adelic invariant for curves of genus at least 2 over number fields and function fields. We calculate this invariant when the genus is equal to…
Covers of surfaces with fixed branch locus
Bas Edixhoven, Robin de Jong, Jan Schepers
Given a connected smooth projective surface X over the complex numbers, together with a simple normal crossings divisor D on it, we study finite normal covers Y of X that are unram…
Local invariants attached to Weierstrass points
Robin de Jong
Let X/S be a hyperelliptic curve of genus g over the spectrum of a discrete valuation ring. Two fundamental numerical invariants are attached to X/S: the valuation of the hyperelli…
Gauss map on the theta divisor and Green's functions
Robin de Jong
In an earlier paper we constructed a Cartier divisor on the theta divisor of a principally polarised abelian variety whose support is precisely the ramification locus of the Gauss…
Theta functions on the theta divisor
Robin de Jong
We show that the gradient and the hessian of the Riemann theta function in dimension n can be combined to give a theta function of order n+1 and modular weight (n+5)/2 defined on t…
Explicit Mumford isomorphism for hyperelliptic curves
Robin de Jong
Using an explicit version of the Mumford isomorphism on the moduli space of hyperelliptic curves we derive a closed formula for the Arakelov-Green function of a hyperelliptic Riema…