A Dimension Formula for the Nucleus of a Veronese Variety
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arXiv
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| Format: | Preprint |
| Published: |
2013
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| _version_ | 1866914672590979072 |
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| author | Gmainer, Johannes Havlicek, Hans |
| author_facet | Gmainer, Johannes Havlicek, Hans |
| contents | The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty. We present an explicit formula for the dimension of this nucleus for arbitrary characteristic of the ground field. As a corollary, we obtain a dimension formula for that subspace in the $t$-th symmetric power of a finite-dimensional vector space $V$ which is spanned by the powers $a^t$ with $\a\in\V$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1304_0092 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A Dimension Formula for the Nucleus of a Veronese Variety Gmainer, Johannes Havlicek, Hans Algebraic Geometry Combinatorics The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty. We present an explicit formula for the dimension of this nucleus for arbitrary characteristic of the ground field. As a corollary, we obtain a dimension formula for that subspace in the $t$-th symmetric power of a finite-dimensional vector space $V$ which is spanned by the powers $a^t$ with $\a\in\V$. |
| title | A Dimension Formula for the Nucleus of a Veronese Variety |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/1304.0092 |