2 papers
math.AG2025
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 det…
math.AG2025
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 guarante…