82 citations · 158 across the 14 of their papers we have counts for
15 papers
Darboux Integrability via Singularities of Invariant Curves at Infinity
Hans-Christian von Bothmer
We extend the computation of the invariant defined in arXiv:2409.01751 to special points on the line at infinity and show that, as in the affine case, its value is deter…
New solutions of the Poincaré Center Problem in degree 3
Hans-Christian von Bothmer
Let be a plane autonomous system and C its configuration of algebraic integral curves. If the singularities of C are quasi-homogeneous we we present new criteria that guarantee…
A survey of the Poincaré Center Problem in degree 3 using finite field heuristics
Hans-Christian Graf v. Bothmer, Jakob Kröker
We compare a heuristic count of components of the center variety in degree 3 with the equivalent count obtained from known families. From this comparison we conjecture that more th…
Focal values of plane cubic centers
Hans-Christian Graf v. Bothmer, Jakob Kröker
We prove that the vanishing of 11 focal values is not sufficient to ensure that a plane cubic system has a center.
Finite Field Experiments (with an Appendix by Stefan Wiedmann)
Hans-Christian Graf v. Bothmer
We explain how to use computer experiments over finite fields to gain heuristic information about the solution set of polynomial equations in characteristic zero. These are notes o…
The Casas-Alvero conjecture for infinitely many degrees
Hans-Christian Graf von Bothmer, Oliver Labs, Josef Schicho +1
Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been…