Timeline for invariant lines avoiding fixed subvarieties
Current License: CC BY-SA 3.0
5 events
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| Apr 23, 2012 at 13:03 | comment | added | naf | Since $g$ is of finite order, you can assume it is given by a diagonal matrix in $SL_{r+1}$ whose entries are roots of unity. It is clear from the definition of the Veronese that $g$ will also act diagonally on $\mathbb{P}^N$, the space corresponding to the Veronese embedding. The diagonal entries are again roots of unity of the same (or smaller) order. Since there are only finitely many such, if $N$ is large there will be many repeated entries. The subspace corresponding to the repeated entries of any root of unity is fixed pointwise. | |
| Apr 22, 2012 at 7:26 | comment | added | reference | Thanks ulrich! Could you please give more details? | |
| Apr 22, 2012 at 7:19 | comment | added | naf | Yes, this is true. Since the order of $g$ is fixed, if $N$ is large there will be linear subspaces $L$ of large dimension preserved pointwise by $d$. Consider any line in such a subspace not meeting the image of $Z$. | |
| Apr 21, 2012 at 20:53 | history | edited | reference | CC BY-SA 3.0 |
added 358 characters in body
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| Apr 21, 2012 at 16:56 | history | asked | reference | CC BY-SA 3.0 |