Timeline for Fixed-point free holomorphic involutions
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2022 at 10:32 | comment | added | Jason Starr | Actually the optimal inequality above is $n+1 > rc$ (a bit better than the inequality I wrote down). If you choose $n+1$ equal to $rc$ and you choose each degree equal to $r$ (so that the sum of the degrees $d$ equals $n+1$), then there are complete intersections with no fixed points. | |
| Jul 13, 2022 at 18:19 | comment | added | Jason Starr | I am just adding some additional information here. Even if you consider actions of finite cyclic groups of arbitrary order $r>1$ on smooth complete intersections of codimension $c$, then the same kind of argument shows that there must be fixed points if $n+1\geq r(c+1)$. A similar combinatorial argument shows there are fixed points if $d\leq n$. For (irreducible) hyper-Kaehler manifolds, there can only be a free action if the dimension of the hyper-Kaehler is congruent to $-2$ module $2r$. | |
| Jul 13, 2022 at 13:41 | comment | added | Mohammad Farajzadeh-Tehrani | This is concrete, thanks. | |
| Jul 12, 2022 at 19:56 | history | answered | abx | CC BY-SA 4.0 |