P. A. Helminck

activity

20162026

most citedTropicalizing abelian covers of algebraic curves

9 citations · 21 across the 18 of their papers we have counts for

collaborators

Showing 2024Show all

3 papers · 1 filter

math.AG2024

A tropical method for solving parametrized polynomial systems

Paul Alexander Helminck, Oskar Henriksson, Yue Ren

We give a framework for constructing generically optimal homotopies for parametrized polynomial systems from tropical data. Here, generically optimal means that the number of paths…

math.NT2024

Toric ranks and component groups of modular curves

Paul Alexander Helminck

Let $p \neq = 2, 3$ be a prime number and let $Γ \subset SL_{2} (Z)$ be a congruence subgroup with modular curve $X_{Γ} / K$ and Jacobian $J (X_{Γ})$ . In this paper we give a…

math.AG2024★ 1 cited

On the topology of the moduli of tropical unramified p-covers

Yassine El Maazouz, Paul Alexander Helminck, Felix Röhrle +2

We study the topology of the moduli space of unramified $Z / p$ -covers of tropical curves of genus $g \geq 2$ , where $p$ is a prime number. We use recent techniques by Chan-…