The Veronese mapping defined as usual on some $P^n$. Then it is certainly regular. I want to prove that the inverse map to this map is also regular.
I have an idea to use projections with respect to some nonzero coordinate (locally) and its multiple to get its preimage and since projections are polynomial maps and hence it is regular. Is my idea correct?
And in this map $f:k[y_0,y_1,...,y_N]\longrightarrow k[x_0,...,x_n]$ sending $y_i$ to a form $M_i$ of degree $d$ how can we say that the kernel is homogeneous ideal?
Thanks for any help