Variants of the Kakeya problem over an algebraically closed field
| Autor: | Slavov, Kaloyan |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Archiv der Mathematik: Volume 103, Issue 3 (2014), Page 267-277 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00013-014-0685-6 |
| Popis: | First, we study constructible subsets of $\A^n_k$ which contain a line in any direction. We classify the smallest such subsets in $\A^3$ of the type $R\cup\{g\neq 0\},$ where $g\in k[x_1,...,x_n]$ is irreducible of degree $d$, and $R\subset V(g)$ is closed. Next, we study subvarieties $X\subset\A^N$ for which the set of directions of lines contined in $X$ has the maximal possible dimension. These are variants of the Kakeya problem in an algebraic geometry context. Comment: Final version, comments of the referee incorporated |
| Databáze: | arXiv |
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