Special loci in the moduli space of quadratic skew products are classified as homogeneous, split or of form (x², y² + b x), and infinite simultaneous preperiodicity of marked points holds iff their good heights coincide, implying orbit closure in a proper subvariety under degree conditions.
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Unlikely intersections in families of polynomial skew products
Special loci in the moduli space of quadratic skew products are classified as homogeneous, split or of form (x², y² + b x), and infinite simultaneous preperiodicity of marked points holds iff their good heights coincide, implying orbit closure in a proper subvariety under degree conditions.