Stable algebraic families of polarized dynamical systems and exceptional extensions
The notion of exceptional maps in arbitrary dimension was recently introduced by Ji, Song, and Xie. In this paper, we introduce exceptional extensions of polarized dynamical systems: a family of systems admitting a positive-dimensional exceptional factor whose generic fiber dynamics have simultaneous local product coordinates with an isotrivial system. We then prove that an algebraic family of polarized endomorphisms of normal projective varieties over a quasi-projective curve is $J$-stable on a nonempty Zariski open subset if and only if it is isotrivial or it is an exceptional extension…
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