Explicit bounds for the finite jet determination problem

Lamel, Bernhard

doi:10.1090/S0002-9947-06-04144-4

Explicit bounds for the finite jet determination problem
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Trans. Amer. Math. Soc. 358 (2006), 3447-3457 Request permission

Abstract:

We introduce biholomorphic invariants for (germs of) rigid holomorphically nondegenerate real hypersurfaces in complex space and show how they can be used to compute explicit bounds on the order of jets for which biholomorphisms of the hypersurface are determined uniquely by their jets. The main result which allows us to derive these bounds is a theorem which shows that solutions of certain singular analytic equations are uniquely determined by their $1$-jet.

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