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- W2963099590 abstract "The Noetherian class is a wide class of functions defined in terms of polynomial partial differential equations. It includes functions appearing naturally in various branches of mathematics (exponential, elliptic, modular, etc.). A conjecture by Khovanskii states that the local geometry of sets defined using Noetherian equations admits effective estimates analogous to the effective global bounds of algebraic geometry. We make a major step in the development of the theory of Noetherian functions by providing an effective upper bound for the local number of isolated solutions of a Noetherian system of equations depending on a parameter $${varepsilon}$$ , which remains valid even when the system degenerates at $${varepsilon = 0}$$ . An estimate of this sort has played the key role in the development of the theory of Pfaffian functions, and is expected to lead to similar results in the Noetherian setting. We illustrate this by deducing from our main result an effective form of the Łojasiewicz inequality for Noetherian functions." @default.
- W2963099590 created "2019-07-30" @default.
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- W2963099590 date "2015-10-01" @default.
- W2963099590 modified "2023-10-09" @default.
- W2963099590 title "Multiplicities of Noetherian Deformations" @default.
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- W2963099590 doi "https://doi.org/10.1007/s00039-015-0340-9" @default.
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