Content deleted Content added
Silvermatsu (talk | contribs) |
TakuyaMurata (talk | contribs) footnote |
||
Line 1:
{{Short description|Invariant cycle theorem}}
In mathematics, the '''local invariant cycle theorem''' was originally a conjecture of Griffiths <ref>{{harvnb|Clemens|1977|loc=Introduction}}</ref><ref>{{harvnb|Griffiths|1970|loc=Conjecture 8.1.}}</ref> which states that, given a surjective [[proper map]] <math>p</math> from a [[Kähler manifold]] <math>X</math> to the unit disk that has maximal rank everywhere except over 0, each cohomology class on <math>p^{-1}(t), t \ne 0</math> is the restriction of some cohomology class on the entire <math>X</math> if the cohomology class is invariant under a circle action (monodromy action); in short,
:<math>\operatorname{H}^*(X) \to \operatorname{H}^*(p^{-1}(t))^{S^1}</math>
is surjective.<ref>Editorial note: the first proof of the theorem was given by Clemens, apparently but this needs to be checked.</ref>
| |||