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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2 Pith papers cite this work. Polarity classification is still indexing.
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Expository account of adelic line bundles, arithmetic positivity, and applications to equidistribution and uniform Bogomolov conjecture.
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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.
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Adelic Line Bundles, Arithmetic Positivity and Diophantine Geometry
Expository account of adelic line bundles, arithmetic positivity, and applications to equidistribution and uniform Bogomolov conjecture.