2
votes
0answers
206 views

2 questions on Nagata's counterexample; $k[f_1,…,f_r]=k[g_1,…,g_s]$ vs. $k(f_1,…,f_r)=k(g_1,…,g_s)$

Let $\{a_{ij}\}$ for $i=1,2,3$, and $j=1,...,16$ be algebraically independent elements over some prime field. Let $k$ be a field containing all $a_{ij}$. Then consider $k^{16}$ as $k$-vector space and ...
7
votes
1answer
321 views

Free group actions on varieties and algebras of coinvariants

Suppose $k$ is an algebraically closed field of characteristic zero and $A$ is a finitely generated commutative associative reduced $k$-algebra. Suppose the group $\mathbb{Z}_2$ acts on $A$ in such a ...
10
votes
2answers
751 views

Symmetric group action on squarefree polynomials

The following dynamical system on polynomials comes mostly from idle curiosity, but I hope it is of some interest. Background Fix some natural number $n$. Let $P$ be the quotient of the polynomial ...