Timeline for finite generation of $G$-equivariant holomorphic maps by polynomials?

6 events

when toggle format	what		by	license	comment
Aug 6, 2012 at 4:01	comment	added	Brett Parker		I emailed Mike Field, who pointed me to the paper `Lifting smooth isotopies of orbit spaces', Publ. I.H.E.S. (51) (1980), 37-135 by GW Schwarz. Proposition 6.8 from there gives that the G-equivariant holomorphic maps are generated by the G-equivariant polynomial maps.
Aug 6, 2012 at 3:57	vote	accept	Brett Parker
Aug 3, 2012 at 14:30	history	edited	Eugene Lerman	CC BY-SA 3.0	added 996 characters in body
Aug 3, 2012 at 14:15	comment	added	Eugene Lerman		Brett, I will edit my answer rather than writing a comment, since the math won't fit in the comment
Aug 3, 2012 at 0:23	comment	added	Brett Parker		Thanks Eugene - I assume you mean that $C^\infty$ equivariant maps are finitely generated as a module over $C^\infty$ equivariant functions. On the other hand, I am pretty sure that in general the generators can't be complex polynomial maps. The counter example is as follows: $V$ and $W$ are $\mathbb C$ with an action of $\mathbb Z_3$ by multiplication by $e^{2\pi i/3}$ and $e^{4\pi i/3}$ respectively. $z\mapsto \bar z$ is not equal to a sum of smooth functions times equivariant complex polynomial maps, because those are generated by the map $z\mapsto z^2$.
Aug 2, 2012 at 18:09	history	answered	Eugene Lerman	CC BY-SA 3.0