Finiteness for Degenerate Polynomials
نویسنده
چکیده
Let MPd denote the space of polynomials f : C → C of degree d ≥ 2, modulo conjugation by Aut(C). Using properties of polynomial trees (as introduced in [DM]), we show that if fn is a divergent sequence of polynomials in MPd, then any subsequential limit of the measures of maximal entropy m(fn) will have finite support. With similar techniques, we observe that the iteration maps {MPd 99K MPdn : n ≥ 1} between GIT-compactifications can be resolved simultaneously with only finitely many blow-ups of MPd.
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