Submission date: 16 November 2015

Abstract:

In this paper we show that the equivalences between certain properties of closed subanalytic sets proved by E. Bierstone and P. Milman in [BM-1] hold for closed sets definable in quasianalytic o-minimal structures. In particular we prove that uniform Chevalley estimate implies a stratification by the diagram of initial exponents and further, Zariski semicontinuity of the diagram of initial exponents. We also show that the stratification by the diagram implies Zariski semicontinuity of Hilbert-Samuel function.

Mathematics Subject Classification: 32B20, 32S05, 14P15

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Full text arXiv 1511.05071: pdf, ps.