F. Vermeulen

activity

20202023

collaborators

11 papers

math.NT2023

Dimension growth for affine varieties

Floris Vermeulen

We prove uniform upper bounds on the number of integral points of bounded height on affine varieties. If $X$ is an irreducible affine variety of degree $d \geq 4$ in $A^{n}$ …

math.AG2023

Scrollar invariants, syzygies and representations of the symmetric group II

Floris Vermeulen

Let $φ : C \to P^{1}$ be a degree $d$ cover of curves. In work by Castryck, Zhao and the author, we showed how one can attach to each partition $λ$ of $d$ a multi-set of scrol…

math.NT2022

Arithmetically equivalent number fields have approximately the same successive minima

Floris Vermeulen

Let $K$ and $K^{'}$ be arithmetically equivalent number fields, both of degree $d$ . We prove that $K$ and $K^{'}$ have the same successive minima, up to a constant depending only on $d$ .…

math.LO2022

Hensel minimality: Geometric criteria for $ℓ$ -h-minimality

Floris Vermeulen

Recently, Cluckers, Halupczok and Rideau-Kikuchi developed a new axiomatic framework for tame non-Archimedean geometry, called Hensel minimality. It was extended to mixed character…

math.NT2022

On abelian covers of the projective line with fixed gonality and many rational points

Xander Faber, Floris Vermeulen

A smooth geometrically connected curve over the finite field $F_{q}$ with gonality $γ$ has at most $γ (q + 1)$ rational points. The first author and Grantham conjectured that…

math.AG2022

Scrollar invariants, syzygies and representations of the symmetric group

Wouter Castryck, Floris Vermeulen, Yongqiang Zhao

We give an explicit minimal graded free resolution, in terms of representations of the symmetric group $S_{d}$ , of a Galois-theoretic configuration of $d$ points in $\mathbb{P}^{d-2}…

Dimension growth for affine varieties

Scrollar invariants, syzygies and representations of the symmetric group II

Arithmetically equivalent number fields have approximately the same successive minima

Hensel minimality: Geometric criteria for ℓ-h-minimality

On abelian covers of the projective line with fixed gonality and many rational points

Scrollar invariants, syzygies and representations of the symmetric group

Hensel minimality: Geometric criteria for $ℓ$ -h-minimality