Nuclei of Normal Rational Curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2013
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| _version_ | 1866909100615401472 |
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| author | Gmainer, Johannes Havlicek, Hans |
| author_facet | Gmainer, Johannes Havlicek, Hans |
| contents | A $k$-nucleus of a normal rational curve in PG$(n,F)$ is the intersection over all $k$-dimensional osculating subspaces of the curve ($k\in\{-1,0,...,n-1\}$). It is well known that for characteristic zero all nuclei are empty. In case of characteristic $p>0$ and $# F\geq n$ the number of non-zero digits in the representation of $n+1$ in base $p$ equals the number of distinct nuclei. An explicit formula for the dimensions of $k$-nuclei is given for $# F\geq k+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_0088 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Nuclei of Normal Rational Curves Gmainer, Johannes Havlicek, Hans Algebraic Geometry Combinatorics A $k$-nucleus of a normal rational curve in PG$(n,F)$ is the intersection over all $k$-dimensional osculating subspaces of the curve ($k\in\{-1,0,...,n-1\}$). It is well known that for characteristic zero all nuclei are empty. In case of characteristic $p>0$ and $# F\geq n$ the number of non-zero digits in the representation of $n+1$ in base $p$ equals the number of distinct nuclei. An explicit formula for the dimensions of $k$-nuclei is given for $# F\geq k+1$. |
| title | Nuclei of Normal Rational Curves |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/1304.0088 |