
#1
Oct1810, 02:46 AM

P: 29

Show the intersection of complex sphere (z1^2+z2^2+z3^2=1) in C^3 and the complex cone (z1^2+z2^2+z3^3=1) in C^3 is a smooth submanifold of C^3.
I am trying to do it using regular level set, but I am not sure which one of (1,0) or (1,1,0) should be set to be the regular value? 



#2
Oct2010, 02:02 PM

P: 491

You have a map from C^3 to R x C. The intersection is the preimage of (1,1,0).



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