[Submitted on 5 Apr 2023 (v1), last revised 24 May 2023 (this version, v2)]
Download the PDF of Naoki Kitazawa’s paper titled Explicit smooth real algebraic functions that may have both compact and non-compact preimages on smooth real algebraic varieties.
overview: In our previous work, we constructed explicit smooth real algebraic functions that may have both compact and non-compact prior images on smooth real algebraic varieties. This article introduces a variation of it. Our result is novel in that we obtain unsuitable smooth real algebraic functions on smooth real algebraic varieties that satisfy explicit conditions on the (non-)compactness of the preimage. Until now, manifolds have only been semi-algebraic. Obviously, this primarily contributes to his two different areas of mathematics. One is the application of differentiable maps to singularity theory and differential topology. More precisely, building a smooth map using the required preimages. Another is real algebraic geometry. More precisely, the explicit construction of smooth real algebraic functions and maps, but in quite a few cases we can know the existence of smooth maps by such a class of maps and consider approximations.
From: Naoki Kitazawa [view email]
Wed, Apr 5, 2023 11:23:09 UTC (39 KB)
Wednesday, May 24, 2023 02:08:02 UTC (42 KB)