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arXiv · 1701.02712

A proof of Kurdyka's conjecture on arc-analytic functions

Janusz Adamus·Hadi Seyedinejad
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Abstract

We prove a conjecture of Kurdyka stating that every arc-symmetric semialgebraic set is precisely the zero locus of an arc-analytic semialgebraic function. This implies, in particular, that arc-symmetric semialgebraic sets are in one-to-one correspondence with radical ideals of the ring of arc-analytic semialgebraic functions.

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Janusz Adamus, Hadi Seyedinejad. 2017-01-10. A proof of Kurdyka's conjecture on arc-analytic functions. https://doi.org/10.1007/s00208-017-1544-0

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