P. A. Helminck

activity

20172021

most citedTropicalizing tame degree three coverings of the projective line

4 citations · 4 across the 2 of their papers we have counts for

collaborators

6 papers

math.AG2021

Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves

Paul Alexander Helminck

In this paper we generalize the $j$ -invariant criterion for the semistable reduction type of an elliptic curve to superelliptic curves $X$ given by $y^{n} = f (x)$ . We first define a…

math.AG2018

Faithful tropicalizations of elliptic curves using minimal models and inflection points

Paul Alexander Helminck

We give an elementary proof of the fact that any elliptic curve $E$ over an algebraically closed non-archimedean field $K$ with residue characteristic $\neq = 2, 3$ and with $v(j(E))…

math.AG2018

Skeletal filtrations of the fundamental group of a non-archimedean curve

Paul Alexander Helminck

In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first generalize a result by Liu and Lorenzini by proving a simultane…

math.AG2018

Semisimple pointed isogeny graphs for abelian varieties

Paul Alexander Helminck

In this paper we show that if $ϕ_{i} : A_{i} \to A$ is a semisimple pointed $K$ -rational $ℓ$ -isogeny graph of order $n$ for a prime $ℓ$ , then the group of $ℓ$ -torsio…

math.AG2018

Torsion points on elliptic curves and tame semistable coverings

P. A. Helminck

In this paper, we study tame Galois coverings of semistable models that arise from torsion points on elliptic curves. These coverings induce Galois morphisms of intersection graphs…

math.AG2017★ 4 cited

Tropicalizing tame degree three coverings of the projective line

Paul Alexander Helminck

In this paper, we study the problem of tropicalizing tame degree three coverings of the projective line. Given any degree three covering $C ⟶ P^{1}$ , we give…