14 citations · 24 across the 12 of their papers we have counts for
12 papers
Arithmetic unlikely intersections in powers of the multiplicative group
Francesco Campagna, Gabriel Andreas Dill, Robert Wilms
Inspired by work of Bugeaud-Corvaja-Zannier, we formulate a conjecture about unlikely intersections in powers of the multiplicative group over the ring of integers in a number fiel…
Intersection numbers as mixed volumes of Newton-Okounkov bodies
Robert Wilms
In this paper we express any intersection number of ample line bundles on an irreducible projective variety as the mixed volume $V(Δ_{Y_\bullet}(L_1),\d…
On the Irreducibility and Distribution of Arithmetic Divisors
Robert Wilms
We introduce the notion of -irreducibility for arithmetic cycles meaning that the degree of its analytic part is small compared to the degree of its irreducible classical part.…
Height coincidences in products of the projective line
Niki Myrto Mavraki, Harry Schmidt, Robert Wilms
We consider hypersurfaces in that contain a generic sequence of small dynamical height with respect to a split map and project onto coordinates. We show th…
On the additivity of Newton-Okounkov bodies
Robert Wilms
We study the additivity of Newton-Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newto-Okounkov body associated to an appropriate fl…
Degeneration of Riemann theta functions and of the Zhang-Kawazumi invariant with applications to a uniform Bogomolov conjecture
Robert Wilms
In this paper we study the degeneration behavior of the norm of the Riemann -function in a family of principally polarized abelian varieties over the punctured complex unit disc…
A uniform quantitative Manin-Mumford theorem for curves over function fields
Nicole Looper, Joseph Silverman, Robert Wilms
We prove that any smooth projective geometrically connected non-isotrivial curve of genus over a one-dimensional function field of any characteristic has at most $16g^2+32…
On arithmetic intersection numbers on self-products of curves
Robert Wilms
We give a close formula for the Néron-Tate height of tautological integral cycles on Jacobians of curves over number fields as well as a new lower bound for the arithmetic self-int…
Some Differential Equations for the Riemann -Function on Jacobians
Robert Wilms
We prove some differential equations for the Riemann theta function associated to the Jacobian of a Riemann surface. The proof is based on some variants of a formula by Fay for the…
New explicit formulas for Faltings' delta-invariant
Robert Wilms
In this paper we give new explicit formulas for Faltings' -invariant in terms of integrals of theta functions, and we deduce an explicit lower bound for only in terms of the…
On Faltings' Delta-Invariant of Hyperelliptic Riemann Surfaces
Robert Wilms
In this paper we prove new explicit formulas for Faltings' -invariant of an arbitrary hyperelliptic Riemann surface. This has several applications: For example we obtain an expl…
The family of ternary cyclotomic polynomials with one free prime
Yves Gallot, Pieter Moree, Robert Wilms
A cyclotomic polynomial Φ_n(x) is said to be ternary if n=pqr with p,q and r distinct odd primes. Ternary cyclotomic polynomials are the simplest ones for which the behaviour of th…