Unique jet determination of CR maps into Nash sets

Let M ⊂ C^N be a real-analytic CR submanifold, M′ ⊂ C^N′ a Nash set and ^EM′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p ∈ M , and for every pair of germs of C^∞ -smooth CR maps f , g : ( M , p ) → M′ , there exists an integer k = k_p such that if f and g have the same k-jets at p, and do not send M into E M′ , then necessarily f = g . Furthermore, the map p ↦ k p may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in C ^N into Nash subsets in C^N′ of D'Angelo finite type, for arbitrary N , N′ ≥ 2.

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Published in: Advances in Mathematics
License: http://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.1016/j.aim.2023.109271