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On differential invariants of geometric structures. (English. Russian original) Zbl 1106.53010
Izv. Math. 70, No. 2, 307-362 (2006); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 2, 99-158 (2006).
The main result of this paper (presented in the Shafarevich seminar) is as follows: If $$P\rightarrow X$$ is a bundle of geometric objects such that the dimension of its generic fibre exceeds that of its base $$X$$, then the number $$t(k)$$ of functionally independent differential invariants of degree $$k$$ at any sufficiently general point tends to infinity as $$k$$ grows.
Also, an asymptotic lower bound for $$t(k)$$ is obtained and a generalization of the previous theorem is given.