We look at degenerating meromorphic families of rational maps on P1-holomorphically parameterized by a punctured disk-and we provide examples where the bifurcation current fails to have a bounded potential in a neighborhood of the puncture. This is in contrast to the recent result of Favre- Gauthier that we always have continuity across the puncture for families of polynomials; and it provides a counterexample to a conjecture posed by Favre in 2016. We explain why our construction fails for polynomial families and for families of rational maps defined over finite extensions of the rationals ℚ.
ASJC Scopus subject areas
- Geometry and Topology