Some topological properties of quotients modulo semisimple algebraic groups
The author proves a general result in Invariant Theory, viz. for a quotient \(\mathbb{C}^n//G\), where \(G\) is a connected complex semisimple algebraic group, the local first homology group at any point in the quotient \(\mathbb{C}^n//G\) is trivial and the local second homology group is finite. Using this, he is able to prove that the completion of the local ring of any point in \(\mathbb{C}^n//G\) is a unique factorization domain (UFD).
scientific article; zbMATH DE number 5609485