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- W4297788222 abstract "We prove that the set of Segre-degenerate points of a real-analytic subvariety $X$ in ${mathbb{C}}^n$ is a closed semianalytic set. It is a subvariety if $X$ is coherent. More precisely, the set of points where the germ of the Segre variety is of dimension $k$ or greater is a closed semianalytic set in general, and for a coherent $X$, it is a real-analytic subvariety of $X$. For a hypersurface $X$ in ${mathbb{C}}^n$, the set of Segre-degenerate points, $X_{[n]}$, is a semianalytic set of dimension at most $2n-4$. If $X$ is coherent, then $X_{[n]}$ is a complex subvariety of (complex) dimension $n-2$. Example hypersurfaces are given showing that $X_{[n]}$ need not be a subvariety and that it also needs not be complex; $X_{[n]}$ can, for instance, be a real line." @default.
- W4297788222 created "2022-10-01" @default.
- W4297788222 creator A5088020961 @default.
- W4297788222 date "2021-02-13" @default.
- W4297788222 modified "2023-10-14" @default.
- W4297788222 title "Segre-Degenerate Points Form a Semianalytic Set" @default.
- W4297788222 doi "https://doi.org/10.48550/arxiv.2102.07025" @default.
- W4297788222 hasPublicationYear "2021" @default.
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